الجبر الأمثلة

$f (x) = {(x^{3} - 2)}^{\frac{1}{5}} + 3$

خطوة 1

اكتب $f (x) = {(x^{3} - 2)}^{\frac{1}{5}} + 3$ في صورة معادلة.

$y = {(x^{3} - 2)}^{\frac{1}{5}} + 3$

خطوة 2

بادِل المتغيرات.

$x = {(y^{3} - 2)}^{\frac{1}{5}} + 3$

خطوة 3

أوجِد قيمة $y$ .

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خطوة 3.1

أعِد كتابة المعادلة في صورة ${(y^{3} - 2)}^{\frac{1}{5}} + 3 = x$ .

${(y^{3} - 2)}^{\frac{1}{5}} + 3 = x$

خطوة 3.2

اطرح $3$ من كلا المتعادلين.

${(y^{3} - 2)}^{\frac{1}{5}} = x - 3$

خطوة 3.3

ارفع كل متعادل إلى القوة $5$ لحذف الأُس الكسري في الطرف الأيسر.

${({(y^{3} - 2)}^{\frac{1}{5}})}^{5} = {(x - 3)}^{5}$

خطوة 3.4

بسّط الأُس.

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خطوة 3.4.1

بسّط الطرف الأيسر.

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خطوة 3.4.1.1

بسّط ${({(y^{3} - 2)}^{\frac{1}{5}})}^{5}$ .

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خطوة 3.4.1.1.1

اضرب الأُسس في ${({(y^{3} - 2)}^{\frac{1}{5}})}^{5}$ .

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خطوة 3.4.1.1.1.1

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

${(y^{3} - 2)}^{\frac{1}{5} \cdot 5} = {(x - 3)}^{5}$

خطوة 3.4.1.1.1.2

ألغِ العامل المشترك لـ $5$ .

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خطوة 3.4.1.1.1.2.1

ألغِ العامل المشترك.

${(y^{3} - 2)}^{\frac{1}{5} \cdot 5} = {(x - 3)}^{5}$

خطوة 3.4.1.1.1.2.2

أعِد كتابة العبارة.

${(y^{3} - 2)}^{1} = {(x - 3)}^{5}$

خطوة 3.4.1.1.2

بسّط.

$y^{3} - 2 = {(x - 3)}^{5}$

خطوة 3.4.2

بسّط الطرف الأيمن.

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خطوة 3.4.2.1

بسّط ${(x - 3)}^{5}$ .

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خطوة 3.4.2.1.1

استخدِم مبرهنة ذات الحدين.

$y^{3} - 2 = x^{5} + 5 x^{4} \cdot - 3 + 10 x^{3} {(- 3)}^{2} + 10 x^{2} {(- 3)}^{3} + 5 x {(- 3)}^{4} + {(- 3)}^{5}$

خطوة 3.4.2.1.2

بسّط كل حد.

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خطوة 3.4.2.1.2.1

اضرب $- 3$ في $5$ .

$y^{3} - 2 = x^{5} - 15 x^{4} + 10 x^{3} {(- 3)}^{2} + 10 x^{2} {(- 3)}^{3} + 5 x {(- 3)}^{4} + {(- 3)}^{5}$

خطوة 3.4.2.1.2.2

ارفع $- 3$ إلى القوة $2$ .

$y^{3} - 2 = x^{5} - 15 x^{4} + 10 x^{3} \cdot 9 + 10 x^{2} {(- 3)}^{3} + 5 x {(- 3)}^{4} + {(- 3)}^{5}$

خطوة 3.4.2.1.2.3

اضرب $9$ في $10$ .

$y^{3} - 2 = x^{5} - 15 x^{4} + 90 x^{3} + 10 x^{2} {(- 3)}^{3} + 5 x {(- 3)}^{4} + {(- 3)}^{5}$

خطوة 3.4.2.1.2.4

ارفع $- 3$ إلى القوة $3$ .

$y^{3} - 2 = x^{5} - 15 x^{4} + 90 x^{3} + 10 x^{2} \cdot - 27 + 5 x {(- 3)}^{4} + {(- 3)}^{5}$

خطوة 3.4.2.1.2.5

اضرب $- 27$ في $10$ .

$y^{3} - 2 = x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 5 x {(- 3)}^{4} + {(- 3)}^{5}$

خطوة 3.4.2.1.2.6

ارفع $- 3$ إلى القوة $4$ .

$y^{3} - 2 = x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 5 x \cdot 81 + {(- 3)}^{5}$

خطوة 3.4.2.1.2.7

اضرب $81$ في $5$ .

$y^{3} - 2 = x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x + {(- 3)}^{5}$

خطوة 3.4.2.1.2.8

ارفع $- 3$ إلى القوة $5$ .

$y^{3} - 2 = x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 243$

خطوة 3.5

أوجِد قيمة $y$ .

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خطوة 3.5.1

انقُل كل الحدود التي لا تحتوي على $y$ إلى المتعادل الأيمن.

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خطوة 3.5.1.1

أضف $2$ إلى كلا المتعادلين.

$y^{3} = x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 243 + 2$

خطوة 3.5.1.2

أضف $- 243$ و $2$ .

$y^{3} = x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241$

خطوة 3.5.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$y = \sqrt[3]{x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241}$

خطوة 4

Replace $y$ with $f^{- 1} (x)$ to show the final answer.

$f^{- 1} (x) = \sqrt[3]{x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241}$

خطوة 5

تحقق مما إذا كانت $f^{- 1} (x) = \sqrt[3]{x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241}$ هي معكوس $f (x) = {(x^{3} - 2)}^{\frac{1}{5}} + 3$ .

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خطوة 5.1

للتحقق من صحة المعكوس، تحقق مما إذا كانتا $f^{- 1} (f (x)) = x$ و $f (f^{- 1} (x)) = x$ .

خطوة 5.2

احسِب قيمة $f^{- 1} (f (x))$ .

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خطوة 5.2.1

عيّن دالة النتيجة المركّبة.

$f^{- 1} (f (x))$

خطوة 5.2.2

احسِب قيمة $f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3)$ باستبدال قيمة $f$ في $f^{- 1}$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{{({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{5} - 15 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{4} + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.3

استخدِم مبرهنة ذات الحدين.

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{{({(x^{3} - 2)}^{\frac{1}{5}})}^{5} + 5 {({(x^{3} - 2)}^{\frac{1}{5}})}^{4} \cdot 3 + 10 {({(x^{3} - 2)}^{\frac{1}{5}})}^{3} \cdot 3^{2} + 10 {({(x^{3} - 2)}^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{4} + 3^{5} - 15 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{4} + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.4

بسّط الحدود.

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خطوة 5.2.4.1

بسّط كل حد.

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خطوة 5.2.4.1.1

اضرب الأُسس في ${({(x^{3} - 2)}^{\frac{1}{5}})}^{5}$ .

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خطوة 5.2.4.1.1.1

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{{(x^{3} - 2)}^{\frac{1}{5} \cdot 5} + 5 {({(x^{3} - 2)}^{\frac{1}{5}})}^{4} \cdot 3 + 10 {({(x^{3} - 2)}^{\frac{1}{5}})}^{3} \cdot 3^{2} + 10 {({(x^{3} - 2)}^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{4} + 3^{5} - 15 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{4} + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.4.1.1.2

ألغِ العامل المشترك لـ $5$ .

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خطوة 5.2.4.1.1.2.1

ألغِ العامل المشترك.

خطوة 5.2.4.1.1.2.2

أعِد كتابة العبارة.

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{(x^{3} - 2) + 5 {({(x^{3} - 2)}^{\frac{1}{5}})}^{4} \cdot 3 + 10 {({(x^{3} - 2)}^{\frac{1}{5}})}^{3} \cdot 3^{2} + 10 {({(x^{3} - 2)}^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{4} + 3^{5} - 15 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{4} + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.4.1.2

بسّط.

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} - 2 + 5 {({(x^{3} - 2)}^{\frac{1}{5}})}^{4} \cdot 3 + 10 {({(x^{3} - 2)}^{\frac{1}{5}})}^{3} \cdot 3^{2} + 10 {({(x^{3} - 2)}^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{4} + 3^{5} - 15 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{4} + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.4.1.3

اضرب الأُسس في ${({(x^{3} - 2)}^{\frac{1}{5}})}^{4}$ .

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خطوة 5.2.4.1.3.1

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} - 2 + 5 {(x^{3} - 2)}^{\frac{1}{5} \cdot 4} \cdot 3 + 10 {({(x^{3} - 2)}^{\frac{1}{5}})}^{3} \cdot 3^{2} + 10 {({(x^{3} - 2)}^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{4} + 3^{5} - 15 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{4} + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.4.1.3.2

اجمع $\frac{1}{5}$ و $4$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} - 2 + 5 {(x^{3} - 2)}^{\frac{4}{5}} \cdot 3 + 10 {({(x^{3} - 2)}^{\frac{1}{5}})}^{3} \cdot 3^{2} + 10 {({(x^{3} - 2)}^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{4} + 3^{5} - 15 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{4} + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.4.1.4

اضرب $3$ في $5$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} - 2 + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 10 {({(x^{3} - 2)}^{\frac{1}{5}})}^{3} \cdot 3^{2} + 10 {({(x^{3} - 2)}^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{4} + 3^{5} - 15 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{4} + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.4.1.5

اضرب الأُسس في ${({(x^{3} - 2)}^{\frac{1}{5}})}^{3}$ .

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خطوة 5.2.4.1.5.1

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} - 2 + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 10 {(x^{3} - 2)}^{\frac{1}{5} \cdot 3} \cdot 3^{2} + 10 {({(x^{3} - 2)}^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{4} + 3^{5} - 15 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{4} + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.4.1.5.2

اجمع $\frac{1}{5}$ و $3$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} - 2 + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 10 {(x^{3} - 2)}^{\frac{3}{5}} \cdot 3^{2} + 10 {({(x^{3} - 2)}^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{4} + 3^{5} - 15 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{4} + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.4.1.6

ارفع $3$ إلى القوة $2$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} - 2 + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 10 {(x^{3} - 2)}^{\frac{3}{5}} \cdot 9 + 10 {({(x^{3} - 2)}^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{4} + 3^{5} - 15 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{4} + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.4.1.7

اضرب $9$ في $10$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} - 2 + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 10 {({(x^{3} - 2)}^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{4} + 3^{5} - 15 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{4} + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.4.1.8

اضرب الأُسس في ${({(x^{3} - 2)}^{\frac{1}{5}})}^{2}$ .

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خطوة 5.2.4.1.8.1

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} - 2 + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 10 {(x^{3} - 2)}^{\frac{1}{5} \cdot 2} \cdot 3^{3} + 5 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{4} + 3^{5} - 15 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{4} + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.4.1.8.2

اجمع $\frac{1}{5}$ و $2$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} - 2 + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 10 {(x^{3} - 2)}^{\frac{2}{5}} \cdot 3^{3} + 5 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{4} + 3^{5} - 15 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{4} + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.4.1.9

ارفع $3$ إلى القوة $3$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} - 2 + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 10 {(x^{3} - 2)}^{\frac{2}{5}} \cdot 27 + 5 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{4} + 3^{5} - 15 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{4} + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.4.1.10

اضرب $27$ في $10$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} - 2 + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 5 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{4} + 3^{5} - 15 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{4} + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.4.1.11

ارفع $3$ إلى القوة $4$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} - 2 + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 5 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 81 + 3^{5} - 15 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{4} + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.4.1.12

اضرب $81$ في $5$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} - 2 + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 3^{5} - 15 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{4} + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.4.1.13

ارفع $3$ إلى القوة $5$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} - 2 + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 243 - 15 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{4} + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.4.2

أضف $- 2$ و $243$ .

خطوة 5.2.5

استخدِم مبرهنة ذات الحدين.

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 ({({(x^{3} - 2)}^{\frac{1}{5}})}^{4} + 4 {({(x^{3} - 2)}^{\frac{1}{5}})}^{3} \cdot 3 + 6 {({(x^{3} - 2)}^{\frac{1}{5}})}^{2} \cdot 3^{2} + 4 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{3} + 3^{4}) + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.6

بسّط الحدود.

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خطوة 5.2.6.1

بسّط كل حد.

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خطوة 5.2.6.1.1

اضرب الأُسس في ${({(x^{3} - 2)}^{\frac{1}{5}})}^{4}$ .

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خطوة 5.2.6.1.1.1

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 ({(x^{3} - 2)}^{\frac{1}{5} \cdot 4} + 4 {({(x^{3} - 2)}^{\frac{1}{5}})}^{3} \cdot 3 + 6 {({(x^{3} - 2)}^{\frac{1}{5}})}^{2} \cdot 3^{2} + 4 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{3} + 3^{4}) + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.6.1.1.2

اجمع $\frac{1}{5}$ و $4$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 ({(x^{3} - 2)}^{\frac{4}{5}} + 4 {({(x^{3} - 2)}^{\frac{1}{5}})}^{3} \cdot 3 + 6 {({(x^{3} - 2)}^{\frac{1}{5}})}^{2} \cdot 3^{2} + 4 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{3} + 3^{4}) + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.6.1.2

اضرب الأُسس في ${({(x^{3} - 2)}^{\frac{1}{5}})}^{3}$ .

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خطوة 5.2.6.1.2.1

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 ({(x^{3} - 2)}^{\frac{4}{5}} + 4 {(x^{3} - 2)}^{\frac{1}{5} \cdot 3} \cdot 3 + 6 {({(x^{3} - 2)}^{\frac{1}{5}})}^{2} \cdot 3^{2} + 4 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{3} + 3^{4}) + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.6.1.2.2

اجمع $\frac{1}{5}$ و $3$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 ({(x^{3} - 2)}^{\frac{4}{5}} + 4 {(x^{3} - 2)}^{\frac{3}{5}} \cdot 3 + 6 {({(x^{3} - 2)}^{\frac{1}{5}})}^{2} \cdot 3^{2} + 4 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{3} + 3^{4}) + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.6.1.3

اضرب $3$ في $4$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 ({(x^{3} - 2)}^{\frac{4}{5}} + 12 {(x^{3} - 2)}^{\frac{3}{5}} + 6 {({(x^{3} - 2)}^{\frac{1}{5}})}^{2} \cdot 3^{2} + 4 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{3} + 3^{4}) + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.6.1.4

اضرب الأُسس في ${({(x^{3} - 2)}^{\frac{1}{5}})}^{2}$ .

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خطوة 5.2.6.1.4.1

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 ({(x^{3} - 2)}^{\frac{4}{5}} + 12 {(x^{3} - 2)}^{\frac{3}{5}} + 6 {(x^{3} - 2)}^{\frac{1}{5} \cdot 2} \cdot 3^{2} + 4 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{3} + 3^{4}) + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.6.1.4.2

اجمع $\frac{1}{5}$ و $2$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 ({(x^{3} - 2)}^{\frac{4}{5}} + 12 {(x^{3} - 2)}^{\frac{3}{5}} + 6 {(x^{3} - 2)}^{\frac{2}{5}} \cdot 3^{2} + 4 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{3} + 3^{4}) + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.6.1.5

ارفع $3$ إلى القوة $2$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 ({(x^{3} - 2)}^{\frac{4}{5}} + 12 {(x^{3} - 2)}^{\frac{3}{5}} + 6 {(x^{3} - 2)}^{\frac{2}{5}} \cdot 9 + 4 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{3} + 3^{4}) + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.6.1.6

اضرب $9$ في $6$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 ({(x^{3} - 2)}^{\frac{4}{5}} + 12 {(x^{3} - 2)}^{\frac{3}{5}} + 54 {(x^{3} - 2)}^{\frac{2}{5}} + 4 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{3} + 3^{4}) + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.6.1.7

ارفع $3$ إلى القوة $3$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 ({(x^{3} - 2)}^{\frac{4}{5}} + 12 {(x^{3} - 2)}^{\frac{3}{5}} + 54 {(x^{3} - 2)}^{\frac{2}{5}} + 4 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 27 + 3^{4}) + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.6.1.8

اضرب $27$ في $4$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 ({(x^{3} - 2)}^{\frac{4}{5}} + 12 {(x^{3} - 2)}^{\frac{3}{5}} + 54 {(x^{3} - 2)}^{\frac{2}{5}} + 108 {(x^{3} - 2)}^{\frac{1}{5}} + 3^{4}) + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.6.1.9

ارفع $3$ إلى القوة $4$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 ({(x^{3} - 2)}^{\frac{4}{5}} + 12 {(x^{3} - 2)}^{\frac{3}{5}} + 54 {(x^{3} - 2)}^{\frac{2}{5}} + 108 {(x^{3} - 2)}^{\frac{1}{5}} + 81) + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.6.2

طبّق خاصية التوزيع.

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 15 (12 {(x^{3} - 2)}^{\frac{3}{5}}) - 15 (54 {(x^{3} - 2)}^{\frac{2}{5}}) - 15 (108 {(x^{3} - 2)}^{\frac{1}{5}}) - 15 \cdot 81 + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.7

بسّط.

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خطوة 5.2.7.1

اضرب $12$ في $- 15$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 15 (54 {(x^{3} - 2)}^{\frac{2}{5}}) - 15 (108 {(x^{3} - 2)}^{\frac{1}{5}}) - 15 \cdot 81 + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.7.2

اضرب $54$ في $- 15$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 15 (108 {(x^{3} - 2)}^{\frac{1}{5}}) - 15 \cdot 81 + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.7.3

اضرب $108$ في $- 15$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 15 \cdot 81 + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.7.4

اضرب $- 15$ في $81$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{3} - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.8

استخدِم مبرهنة ذات الحدين.

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 ({({(x^{3} - 2)}^{\frac{1}{5}})}^{3} + 3 {({(x^{3} - 2)}^{\frac{1}{5}})}^{2} \cdot 3 + 3 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{2} + 3^{3}) - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.9

بسّط الحدود.

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خطوة 5.2.9.1

بسّط كل حد.

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خطوة 5.2.9.1.1

اضرب الأُسس في ${({(x^{3} - 2)}^{\frac{1}{5}})}^{3}$ .

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خطوة 5.2.9.1.1.1

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 ({(x^{3} - 2)}^{\frac{1}{5} \cdot 3} + 3 {({(x^{3} - 2)}^{\frac{1}{5}})}^{2} \cdot 3 + 3 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{2} + 3^{3}) - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.9.1.1.2

اجمع $\frac{1}{5}$ و $3$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 ({(x^{3} - 2)}^{\frac{3}{5}} + 3 {({(x^{3} - 2)}^{\frac{1}{5}})}^{2} \cdot 3 + 3 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{2} + 3^{3}) - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.9.1.2

اضرب الأُسس في ${({(x^{3} - 2)}^{\frac{1}{5}})}^{2}$ .

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خطوة 5.2.9.1.2.1

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 ({(x^{3} - 2)}^{\frac{3}{5}} + 3 {(x^{3} - 2)}^{\frac{1}{5} \cdot 2} \cdot 3 + 3 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{2} + 3^{3}) - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.9.1.2.2

اجمع $\frac{1}{5}$ و $2$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 ({(x^{3} - 2)}^{\frac{3}{5}} + 3 {(x^{3} - 2)}^{\frac{2}{5}} \cdot 3 + 3 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{2} + 3^{3}) - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.9.1.3

اضرب $3$ في $3$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 ({(x^{3} - 2)}^{\frac{3}{5}} + 9 {(x^{3} - 2)}^{\frac{2}{5}} + 3 {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3^{2} + 3^{3}) - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.9.1.4

اضرب $3$ في $3^{2}$ بجمع الأُسس.

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خطوة 5.2.9.1.4.1

انقُل $3^{2}$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 ({(x^{3} - 2)}^{\frac{3}{5}} + 9 {(x^{3} - 2)}^{\frac{2}{5}} + 3^{2} \cdot (3 {(x^{3} - 2)}^{\frac{1}{5}}) + 3^{3}) - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.9.1.4.2

اضرب $3^{2}$ في $3$ .

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خطوة 5.2.9.1.4.2.1

ارفع $3$ إلى القوة $1$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 ({(x^{3} - 2)}^{\frac{3}{5}} + 9 {(x^{3} - 2)}^{\frac{2}{5}} + 3^{2} \cdot (3 {(x^{3} - 2)}^{\frac{1}{5}}) + 3^{3}) - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.9.1.4.2.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 ({(x^{3} - 2)}^{\frac{3}{5}} + 9 {(x^{3} - 2)}^{\frac{2}{5}} + 3^{2 + 1} {(x^{3} - 2)}^{\frac{1}{5}} + 3^{3}) - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.9.1.4.3

أضف $2$ و $1$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 ({(x^{3} - 2)}^{\frac{3}{5}} + 9 {(x^{3} - 2)}^{\frac{2}{5}} + 3^{3} {(x^{3} - 2)}^{\frac{1}{5}} + 3^{3}) - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.9.1.5

ارفع $3$ إلى القوة $3$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 ({(x^{3} - 2)}^{\frac{3}{5}} + 9 {(x^{3} - 2)}^{\frac{2}{5}} + 27 {(x^{3} - 2)}^{\frac{1}{5}} + 3^{3}) - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.9.1.6

ارفع $3$ إلى القوة $3$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 ({(x^{3} - 2)}^{\frac{3}{5}} + 9 {(x^{3} - 2)}^{\frac{2}{5}} + 27 {(x^{3} - 2)}^{\frac{1}{5}} + 27) - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.9.2

طبّق خاصية التوزيع.

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 90 (9 {(x^{3} - 2)}^{\frac{2}{5}}) + 90 (27 {(x^{3} - 2)}^{\frac{1}{5}}) + 90 \cdot 27 - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.10

بسّط.

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خطوة 5.2.10.1

اضرب $9$ في $90$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 90 (27 {(x^{3} - 2)}^{\frac{1}{5}}) + 90 \cdot 27 - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.10.2

اضرب $27$ في $90$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} + 90 \cdot 27 - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.10.3

اضرب $90$ في $27$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} + 2430 - 270 {({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2} + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.11

أعِد كتابة ${({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2}$ بالصيغة $({(x^{3} - 2)}^{\frac{1}{5}} + 3) ({(x^{3} - 2)}^{\frac{1}{5}} + 3)$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} + 2430 - 270 (({(x^{3} - 2)}^{\frac{1}{5}} + 3) ({(x^{3} - 2)}^{\frac{1}{5}} + 3)) + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.12

وسّع $({(x^{3} - 2)}^{\frac{1}{5}} + 3) ({(x^{3} - 2)}^{\frac{1}{5}} + 3)$ باستخدام طريقة "الأول، الخارجي، الداخلي، الأخير".

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خطوة 5.2.12.1

طبّق خاصية التوزيع.

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} + 2430 - 270 ({(x^{3} - 2)}^{\frac{1}{5}} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) + 3 ({(x^{3} - 2)}^{\frac{1}{5}} + 3)) + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.12.2

طبّق خاصية التوزيع.

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} + 2430 - 270 ({(x^{3} - 2)}^{\frac{1}{5}} {(x^{3} - 2)}^{\frac{1}{5}} + {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3 + 3 ({(x^{3} - 2)}^{\frac{1}{5}} + 3)) + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.12.3

طبّق خاصية التوزيع.

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} + 2430 - 270 ({(x^{3} - 2)}^{\frac{1}{5}} {(x^{3} - 2)}^{\frac{1}{5}} + {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3 + 3 {(x^{3} - 2)}^{\frac{1}{5}} + 3 \cdot 3) + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.13

بسّط ووحّد الحدود المتشابهة.

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خطوة 5.2.13.1

بسّط كل حد.

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خطوة 5.2.13.1.1

اضرب ${(x^{3} - 2)}^{\frac{1}{5}}$ في ${(x^{3} - 2)}^{\frac{1}{5}}$ بجمع الأُسس.

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خطوة 5.2.13.1.1.1

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} + 2430 - 270 ({(x^{3} - 2)}^{\frac{1}{5} + \frac{1}{5}} + {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3 + 3 {(x^{3} - 2)}^{\frac{1}{5}} + 3 \cdot 3) + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.13.1.1.2

اجمع البسوط على القاسم المشترك.

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} + 2430 - 270 ({(x^{3} - 2)}^{\frac{1 + 1}{5}} + {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3 + 3 {(x^{3} - 2)}^{\frac{1}{5}} + 3 \cdot 3) + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.13.1.1.3

أضف $1$ و $1$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} + 2430 - 270 ({(x^{3} - 2)}^{\frac{2}{5}} + {(x^{3} - 2)}^{\frac{1}{5}} \cdot 3 + 3 {(x^{3} - 2)}^{\frac{1}{5}} + 3 \cdot 3) + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.13.1.2

انقُل $3$ إلى يسار ${(x^{3} - 2)}^{\frac{1}{5}}$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} + 2430 - 270 ({(x^{3} - 2)}^{\frac{2}{5}} + 3 \cdot {(x^{3} - 2)}^{\frac{1}{5}} + 3 {(x^{3} - 2)}^{\frac{1}{5}} + 3 \cdot 3) + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.13.1.3

اضرب $3$ في $3$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} + 2430 - 270 ({(x^{3} - 2)}^{\frac{2}{5}} + 3 {(x^{3} - 2)}^{\frac{1}{5}} + 3 {(x^{3} - 2)}^{\frac{1}{5}} + 9) + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.13.2

أضف $3 {(x^{3} - 2)}^{\frac{1}{5}}$ و $3 {(x^{3} - 2)}^{\frac{1}{5}}$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} + 2430 - 270 ({(x^{3} - 2)}^{\frac{2}{5}} + 6 {(x^{3} - 2)}^{\frac{1}{5}} + 9) + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.14

طبّق خاصية التوزيع.

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} + 2430 - 270 {(x^{3} - 2)}^{\frac{2}{5}} - 270 (6 {(x^{3} - 2)}^{\frac{1}{5}}) - 270 \cdot 9 + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.15

بسّط.

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خطوة 5.2.15.1

اضرب $6$ في $- 270$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} + 2430 - 270 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 270 \cdot 9 + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.15.2

اضرب $- 270$ في $9$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} + 2430 - 270 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 2430 + 405 ({(x^{3} - 2)}^{\frac{1}{5}} + 3) - 241}$

خطوة 5.2.16

طبّق خاصية التوزيع.

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} + 2430 - 270 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 2430 + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 405 \cdot 3 - 241}$

خطوة 5.2.17

اضرب $405$ في $3$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 15 {(x^{3} - 2)}^{\frac{4}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 15 {(x^{3} - 2)}^{\frac{4}{5}} - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} + 2430 - 270 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 2430 + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 1215 - 241}$

خطوة 5.2.18

اطرح $15 {(x^{3} - 2)}^{\frac{4}{5}}$ من $15 {(x^{3} - 2)}^{\frac{4}{5}}$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 + 0 - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} + 2430 - 270 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 2430 + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 1215 - 241}$

خطوة 5.2.19

أضف $x^{3}$ و $0$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 180 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} + 2430 - 270 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 2430 + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 1215 - 241}$

خطوة 5.2.20

اطرح $180 {(x^{3} - 2)}^{\frac{3}{5}}$ من $90 {(x^{3} - 2)}^{\frac{3}{5}}$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 270 {(x^{3} - 2)}^{\frac{2}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 90 {(x^{3} - 2)}^{\frac{3}{5}} - 810 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} + 2430 - 270 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 2430 + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 1215 - 241}$

خطوة 5.2.21

اطرح $810 {(x^{3} - 2)}^{\frac{2}{5}}$ من $270 {(x^{3} - 2)}^{\frac{2}{5}}$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 241 - 90 {(x^{3} - 2)}^{\frac{3}{5}} - 540 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} + 2430 - 270 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 2430 + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 1215 - 241}$

خطوة 5.2.22

اطرح $1620 {(x^{3} - 2)}^{\frac{1}{5}}$ من $405 {(x^{3} - 2)}^{\frac{1}{5}}$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 241 - 90 {(x^{3} - 2)}^{\frac{3}{5}} - 540 {(x^{3} - 2)}^{\frac{2}{5}} - 1215 {(x^{3} - 2)}^{\frac{1}{5}} - 1215 + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} + 2430 - 270 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 2430 + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 1215 - 241}$

خطوة 5.2.23

بسّط عن طريق الجمع والطرح.

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خطوة 5.2.23.1

اطرح $1215$ من $241$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} - 974 - 90 {(x^{3} - 2)}^{\frac{3}{5}} - 540 {(x^{3} - 2)}^{\frac{2}{5}} - 1215 {(x^{3} - 2)}^{\frac{1}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} + 2430 - 270 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 2430 + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 1215 - 241}$

خطوة 5.2.23.2

أضف $- 974$ و $2430$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 1456 - 90 {(x^{3} - 2)}^{\frac{3}{5}} - 540 {(x^{3} - 2)}^{\frac{2}{5}} - 1215 {(x^{3} - 2)}^{\frac{1}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} - 270 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} - 2430 + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 1215 - 241}$

خطوة 5.2.23.3

اطرح $2430$ من $1456$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} - 974 - 90 {(x^{3} - 2)}^{\frac{3}{5}} - 540 {(x^{3} - 2)}^{\frac{2}{5}} - 1215 {(x^{3} - 2)}^{\frac{1}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} - 270 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} + 1215 - 241}$

خطوة 5.2.23.4

أضف $- 974$ و $1215$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 241 - 90 {(x^{3} - 2)}^{\frac{3}{5}} - 540 {(x^{3} - 2)}^{\frac{2}{5}} - 1215 {(x^{3} - 2)}^{\frac{1}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} - 270 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}} - 241}$

خطوة 5.2.23.5

اطرح $241$ من $241$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 0 - 90 {(x^{3} - 2)}^{\frac{3}{5}} - 540 {(x^{3} - 2)}^{\frac{2}{5}} - 1215 {(x^{3} - 2)}^{\frac{1}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} - 270 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}}}$

خطوة 5.2.23.6

أضف $x^{3}$ و $0$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} - 90 {(x^{3} - 2)}^{\frac{3}{5}} - 540 {(x^{3} - 2)}^{\frac{2}{5}} - 1215 {(x^{3} - 2)}^{\frac{1}{5}} + 90 {(x^{3} - 2)}^{\frac{3}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} - 270 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}}}$

خطوة 5.2.24

أضف $- 90 {(x^{3} - 2)}^{\frac{3}{5}}$ و $90 {(x^{3} - 2)}^{\frac{3}{5}}$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 0 - 540 {(x^{3} - 2)}^{\frac{2}{5}} - 1215 {(x^{3} - 2)}^{\frac{1}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} - 270 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}}}$

خطوة 5.2.25

أضف $x^{3}$ و $0$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} - 540 {(x^{3} - 2)}^{\frac{2}{5}} - 1215 {(x^{3} - 2)}^{\frac{1}{5}} + 810 {(x^{3} - 2)}^{\frac{2}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} - 270 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}}}$

خطوة 5.2.26

أضف $- 540 {(x^{3} - 2)}^{\frac{2}{5}}$ و $810 {(x^{3} - 2)}^{\frac{2}{5}}$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 270 {(x^{3} - 2)}^{\frac{2}{5}} - 1215 {(x^{3} - 2)}^{\frac{1}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} - 270 {(x^{3} - 2)}^{\frac{2}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}}}$

خطوة 5.2.27

اطرح $270 {(x^{3} - 2)}^{\frac{2}{5}}$ من $270 {(x^{3} - 2)}^{\frac{2}{5}}$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 0 - 1215 {(x^{3} - 2)}^{\frac{1}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}}}$

خطوة 5.2.28

أضف $x^{3}$ و $0$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} - 1215 {(x^{3} - 2)}^{\frac{1}{5}} + 2430 {(x^{3} - 2)}^{\frac{1}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}}}$

خطوة 5.2.29

أضف $- 1215 {(x^{3} - 2)}^{\frac{1}{5}}$ و $2430 {(x^{3} - 2)}^{\frac{1}{5}}$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 1215 {(x^{3} - 2)}^{\frac{1}{5}} - 1620 {(x^{3} - 2)}^{\frac{1}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}}}$

خطوة 5.2.30

اطرح $1620 {(x^{3} - 2)}^{\frac{1}{5}}$ من $1215 {(x^{3} - 2)}^{\frac{1}{5}}$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} - 405 {(x^{3} - 2)}^{\frac{1}{5}} + 405 {(x^{3} - 2)}^{\frac{1}{5}}}$

خطوة 5.2.31

أضف $- 405 {(x^{3} - 2)}^{\frac{1}{5}}$ و $405 {(x^{3} - 2)}^{\frac{1}{5}}$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3} + 0}$

خطوة 5.2.32

أضف $x^{3}$ و $0$ .

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = \sqrt[3]{x^{3}}$

خطوة 5.2.33

أخرِج الحدود من تحت الجذر، بافتراض أنها أعداد حقيقية.

$f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3) = x$

خطوة 5.3

احسِب قيمة $f (f^{- 1} (x))$ .

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خطوة 5.3.1

عيّن دالة النتيجة المركّبة.

$f (f^{- 1} (x))$

خطوة 5.3.2

احسِب قيمة $f (\sqrt[3]{x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241})$ باستبدال قيمة $f^{- 1}$ في $f$ .

$f (\sqrt[3]{x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241}) = {({(\sqrt[3]{x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241})}^{3} - 2)}^{\frac{1}{5}} + 3$

خطوة 5.3.3

بسّط كل حد.

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خطوة 5.3.3.1

أعِد كتابة ${\sqrt[3]{x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241}}^{3}$ بالصيغة $x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241$ .

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خطوة 5.3.3.1.1

استخدِم $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ لكتابة $\sqrt[3]{x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241}$ في صورة ${(x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241)}^{\frac{1}{3}}$ .

$f (\sqrt[3]{x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241}) = {({({(x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241)}^{\frac{1}{3}})}^{3} - 2)}^{\frac{1}{5}} + 3$

خطوة 5.3.3.1.2

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

$f (\sqrt[3]{x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241}) = {({(x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241)}^{\frac{1}{3} \cdot 3} - 2)}^{\frac{1}{5}} + 3$

خطوة 5.3.3.1.3

اجمع $\frac{1}{3}$ و $3$ .

$f (\sqrt[3]{x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241}) = {({(x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241)}^{\frac{3}{3}} - 2)}^{\frac{1}{5}} + 3$

خطوة 5.3.3.1.4

ألغِ العامل المشترك لـ $3$ .

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خطوة 5.3.3.1.4.1

ألغِ العامل المشترك.

$f (\sqrt[3]{x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241}) = {({(x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241)}^{\frac{3}{3}} - 2)}^{\frac{1}{5}} + 3$

خطوة 5.3.3.1.4.2

أعِد كتابة العبارة.

$f (\sqrt[3]{x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241}) = {((x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241) - 2)}^{\frac{1}{5}} + 3$

خطوة 5.3.3.1.5

بسّط.

$f (\sqrt[3]{x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241}) = {(x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241 - 2)}^{\frac{1}{5}} + 3$

خطوة 5.3.3.2

اطرح $2$ من $- 241$ .

$f (\sqrt[3]{x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241}) = {(x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 243)}^{\frac{1}{5}} + 3$

خطوة 5.4

بما أن $f^{- 1} (f (x)) = x$ و $f (f^{- 1} (x)) = x$ ، إذن $f^{- 1} (x) = \sqrt[3]{x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241}$ هي معكوس $f (x) = {(x^{3} - 2)}^{\frac{1}{5}} + 3$ .

$f^{- 1} (x) = \sqrt[3]{x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241}$