एलजेब्रा उदाहरण

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

चरण 1

$f (x) = {(x^{3} - 2)}^{\frac{1}{5}} + 3$ को एक समीकरण के रूप में लिखें.

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

चरण 2

चर को एकदूसरे के साथ बदलें.

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

चरण 3

$y$ के लिए हल करें.

और स्टेप्स के लिए टैप करें…

चरण 3.1

समीकरण को ${(y^{3} - 2)}^{\frac{1}{5}} + 3 = x$ के रूप में फिर से लिखें.

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

चरण 3.2

समीकरण के दोनों पक्षों से $3$ घटाएं.

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

चरण 3.3

बाईं ओर के भिन्नात्मक घातांक को समाप्त करने के लिए समीकरण के प्रत्येक पक्ष को $5$ की घात तक बढ़ाएँ.

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

चरण 3.4

घातांक को सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 3.4.1

बाईं ओर को सरल बनाएंं.

और स्टेप्स के लिए टैप करें…

चरण 3.4.1.1

${({(y^{3} - 2)}^{\frac{1}{5}})}^{5}$ को सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 3.4.1.1.1

घातांक को ${({(y^{3} - 2)}^{\frac{1}{5}})}^{5}$ में गुणा करें.

और स्टेप्स के लिए टैप करें…

चरण 3.4.1.1.1.1

घात नियम लागू करें और घातांक गुणा करें, ${(a^{m})}^{n} = a^{m n}$ .

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

चरण 3.4.1.1.1.2

$5$ का उभयनिष्ठ गुणनखंड रद्द करें.

और स्टेप्स के लिए टैप करें…

चरण 3.4.1.1.1.2.1

उभयनिष्ठ गुणनखंड रद्द करें.

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

चरण 3.4.1.1.1.2.2

व्यंजक को फिर से लिखें.

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

चरण 3.4.1.1.2

सरल करें.

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

चरण 3.4.2

दाईं ओर को सरल बनाएंं.

और स्टेप्स के लिए टैप करें…

चरण 3.4.2.1

${(x - 3)}^{5}$ को सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 3.4.2.1.1

द्विपद प्रमेय का प्रयोग करें.

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

चरण 3.4.2.1.2

प्रत्येक पद को सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 3.4.2.1.2.1

$- 3$ को $5$ से गुणा करें.

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

चरण 3.4.2.1.2.2

$- 3$ को $2$ के घात तक बढ़ाएं.

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

चरण 3.4.2.1.2.3

$9$ को $10$ से गुणा करें.

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

चरण 3.4.2.1.2.4

$- 3$ को $3$ के घात तक बढ़ाएं.

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

चरण 3.4.2.1.2.5

$- 27$ को $10$ से गुणा करें.

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

चरण 3.4.2.1.2.6

$- 3$ को $4$ के घात तक बढ़ाएं.

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

चरण 3.4.2.1.2.7

$81$ को $5$ से गुणा करें.

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

चरण 3.4.2.1.2.8

$- 3$ को $5$ के घात तक बढ़ाएं.

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

चरण 3.5

$y$ के लिए हल करें.

और स्टेप्स के लिए टैप करें…

चरण 3.5.1

$y$ वाले सभी पदों को समीकरण के दाईं ओर ले जाएं.

और स्टेप्स के लिए टैप करें…

चरण 3.5.1.1

समीकरण के दोनों पक्षों में $2$ जोड़ें.

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

चरण 3.5.1.2

$- 243$ और $2$ जोड़ें.

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

चरण 3.5.2

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

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

चरण 4

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

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

चरण 5

सत्यापित करें कि क्या $f^{- 1} (x) = \sqrt[3]{x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241}$ , $f (x) = {(x^{3} - 2)}^{\frac{1}{5}} + 3$ का व्युत्क्रम है.

और स्टेप्स के लिए टैप करें…

चरण 5.1

व्युत्क्रम सत्यापित करने के लिए, जांचें कि क्या $f^{- 1} (f (x)) = x$ और $f (f^{- 1} (x)) = x$ .

चरण 5.2

$f^{- 1} (f (x))$ का मान ज्ञात करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.1

समग्र परिणाम फलन सेट करें.

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

चरण 5.2.2

$f^{- 1}$ में $f$ का मान प्रतिस्थापित करके $f^{- 1} ({(x^{3} - 2)}^{\frac{1}{5}} + 3)$ का मान ज्ञात करें.

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

चरण 5.2.3

द्विपद प्रमेय का प्रयोग करें.

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

चरण 5.2.4

पदों को सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.4.1

प्रत्येक पद को सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.4.1.1

घातांक को ${({(x^{3} - 2)}^{\frac{1}{5}})}^{5}$ में गुणा करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.4.1.1.1

घात नियम लागू करें और घातांक गुणा करें, ${(a^{m})}^{n} = a^{m n}$ .

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

चरण 5.2.4.1.1.2

$5$ का उभयनिष्ठ गुणनखंड रद्द करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.4.1.1.2.1

उभयनिष्ठ गुणनखंड रद्द करें.

चरण 5.2.4.1.1.2.2

व्यंजक को फिर से लिखें.

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

चरण 5.2.4.1.2

सरल करें.

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

चरण 5.2.4.1.3

घातांक को ${({(x^{3} - 2)}^{\frac{1}{5}})}^{4}$ में गुणा करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.4.1.3.1

घात नियम लागू करें और घातांक गुणा करें, ${(a^{m})}^{n} = a^{m n}$ .

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

चरण 5.2.4.1.3.2

$\frac{1}{5}$ और $4$ को मिलाएं.

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

चरण 5.2.4.1.4

$3$ को $5$ से गुणा करें.

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

चरण 5.2.4.1.5

घातांक को ${({(x^{3} - 2)}^{\frac{1}{5}})}^{3}$ में गुणा करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.4.1.5.1

घात नियम लागू करें और घातांक गुणा करें, ${(a^{m})}^{n} = a^{m n}$ .

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

चरण 5.2.4.1.5.2

$\frac{1}{5}$ और $3$ को मिलाएं.

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

चरण 5.2.4.1.6

$3$ को $2$ के घात तक बढ़ाएं.

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

चरण 5.2.4.1.7

$9$ को $10$ से गुणा करें.

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

चरण 5.2.4.1.8

घातांक को ${({(x^{3} - 2)}^{\frac{1}{5}})}^{2}$ में गुणा करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.4.1.8.1

घात नियम लागू करें और घातांक गुणा करें, ${(a^{m})}^{n} = a^{m n}$ .

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

चरण 5.2.4.1.8.2

$\frac{1}{5}$ और $2$ को मिलाएं.

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

चरण 5.2.4.1.9

$3$ को $3$ के घात तक बढ़ाएं.

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

चरण 5.2.4.1.10

$27$ को $10$ से गुणा करें.

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

चरण 5.2.4.1.11

$3$ को $4$ के घात तक बढ़ाएं.

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

चरण 5.2.4.1.12

$81$ को $5$ से गुणा करें.

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

चरण 5.2.4.1.13

$3$ को $5$ के घात तक बढ़ाएं.

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

चरण 5.2.4.2

$- 2$ और $243$ जोड़ें.

चरण 5.2.5

द्विपद प्रमेय का प्रयोग करें.

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

चरण 5.2.6

पदों को सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.6.1

प्रत्येक पद को सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.6.1.1

घातांक को ${({(x^{3} - 2)}^{\frac{1}{5}})}^{4}$ में गुणा करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.6.1.1.1

घात नियम लागू करें और घातांक गुणा करें, ${(a^{m})}^{n} = a^{m n}$ .

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

चरण 5.2.6.1.1.2

$\frac{1}{5}$ और $4$ को मिलाएं.

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

चरण 5.2.6.1.2

घातांक को ${({(x^{3} - 2)}^{\frac{1}{5}})}^{3}$ में गुणा करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.6.1.2.1

घात नियम लागू करें और घातांक गुणा करें, ${(a^{m})}^{n} = a^{m n}$ .

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

चरण 5.2.6.1.2.2

$\frac{1}{5}$ और $3$ को मिलाएं.

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

चरण 5.2.6.1.3

$3$ को $4$ से गुणा करें.

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

चरण 5.2.6.1.4

घातांक को ${({(x^{3} - 2)}^{\frac{1}{5}})}^{2}$ में गुणा करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.6.1.4.1

घात नियम लागू करें और घातांक गुणा करें, ${(a^{m})}^{n} = a^{m n}$ .

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

चरण 5.2.6.1.4.2

$\frac{1}{5}$ और $2$ को मिलाएं.

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

चरण 5.2.6.1.5

$3$ को $2$ के घात तक बढ़ाएं.

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

चरण 5.2.6.1.6

$9$ को $6$ से गुणा करें.

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

चरण 5.2.6.1.7

$3$ को $3$ के घात तक बढ़ाएं.

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

चरण 5.2.6.1.8

$27$ को $4$ से गुणा करें.

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

चरण 5.2.6.1.9

$3$ को $4$ के घात तक बढ़ाएं.

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

चरण 5.2.6.2

वितरण गुणधर्म लागू करें.

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

चरण 5.2.7

सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.7.1

$12$ को $- 15$ से गुणा करें.

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

चरण 5.2.7.2

$54$ को $- 15$ से गुणा करें.

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

चरण 5.2.7.3

$108$ को $- 15$ से गुणा करें.

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

चरण 5.2.7.4

$- 15$ को $81$ से गुणा करें.

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

चरण 5.2.8

द्विपद प्रमेय का प्रयोग करें.

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

चरण 5.2.9

पदों को सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.9.1

प्रत्येक पद को सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.9.1.1

घातांक को ${({(x^{3} - 2)}^{\frac{1}{5}})}^{3}$ में गुणा करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.9.1.1.1

घात नियम लागू करें और घातांक गुणा करें, ${(a^{m})}^{n} = a^{m n}$ .

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

चरण 5.2.9.1.1.2

$\frac{1}{5}$ और $3$ को मिलाएं.

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

चरण 5.2.9.1.2

घातांक को ${({(x^{3} - 2)}^{\frac{1}{5}})}^{2}$ में गुणा करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.9.1.2.1

घात नियम लागू करें और घातांक गुणा करें, ${(a^{m})}^{n} = a^{m n}$ .

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

चरण 5.2.9.1.2.2

$\frac{1}{5}$ और $2$ को मिलाएं.

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

चरण 5.2.9.1.3

$3$ को $3$ से गुणा करें.

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

चरण 5.2.9.1.4

घातांक जोड़कर $3$ को $3^{2}$ से गुणा करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.9.1.4.1

$3^{2}$ ले जाएं.

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

चरण 5.2.9.1.4.2

$3^{2}$ को $3$ से गुणा करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.9.1.4.2.1

$3$ को $1$ के घात तक बढ़ाएं.

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

चरण 5.2.9.1.4.2.2

घातांकों को संयोजित करने के लिए घात नियम $a^{m} a^{n} = a^{m + n}$ का उपयोग करें.

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

चरण 5.2.9.1.4.3

$2$ और $1$ जोड़ें.

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

चरण 5.2.9.1.5

$3$ को $3$ के घात तक बढ़ाएं.

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

चरण 5.2.9.1.6

$3$ को $3$ के घात तक बढ़ाएं.

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

चरण 5.2.9.2

वितरण गुणधर्म लागू करें.

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

चरण 5.2.10

सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.10.1

$9$ को $90$ से गुणा करें.

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

चरण 5.2.10.2

$27$ को $90$ से गुणा करें.

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

चरण 5.2.10.3

$90$ को $27$ से गुणा करें.

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

चरण 5.2.11

${({(x^{3} - 2)}^{\frac{1}{5}} + 3)}^{2}$ को $({(x^{3} - 2)}^{\frac{1}{5}} + 3) ({(x^{3} - 2)}^{\frac{1}{5}} + 3)$ के रूप में फिर से लिखें.

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

चरण 5.2.12

FOIL विधि का उपयोग करके $({(x^{3} - 2)}^{\frac{1}{5}} + 3) ({(x^{3} - 2)}^{\frac{1}{5}} + 3)$ का प्रसार करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.12.1

वितरण गुणधर्म लागू करें.

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

चरण 5.2.12.2

वितरण गुणधर्म लागू करें.

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

चरण 5.2.12.3

वितरण गुणधर्म लागू करें.

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

चरण 5.2.13

समान पदों को सरल और संयोजित करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.13.1

प्रत्येक पद को सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.13.1.1

घातांक जोड़कर ${(x^{3} - 2)}^{\frac{1}{5}}$ को ${(x^{3} - 2)}^{\frac{1}{5}}$ से गुणा करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.13.1.1.1

घातांकों को संयोजित करने के लिए घात नियम $a^{m} a^{n} = a^{m + n}$ का उपयोग करें.

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

चरण 5.2.13.1.1.2

सामान्य भाजक पर न्यूमेरेटरों को जोड़ें.

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

चरण 5.2.13.1.1.3

$1$ और $1$ जोड़ें.

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

चरण 5.2.13.1.2

$3$ को ${(x^{3} - 2)}^{\frac{1}{5}}$ के बाईं ओर ले जाएं.

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

चरण 5.2.13.1.3

$3$ को $3$ से गुणा करें.

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

चरण 5.2.13.2

$3 {(x^{3} - 2)}^{\frac{1}{5}}$ और $3 {(x^{3} - 2)}^{\frac{1}{5}}$ जोड़ें.

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

चरण 5.2.14

वितरण गुणधर्म लागू करें.

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

चरण 5.2.15

सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.15.1

$6$ को $- 270$ से गुणा करें.

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

चरण 5.2.15.2

$- 270$ को $9$ से गुणा करें.

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

चरण 5.2.16

वितरण गुणधर्म लागू करें.

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

चरण 5.2.17

$405$ को $3$ से गुणा करें.

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

चरण 5.2.18

$15 {(x^{3} - 2)}^{\frac{4}{5}}$ में से $15 {(x^{3} - 2)}^{\frac{4}{5}}$ घटाएं.

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

चरण 5.2.19

$x^{3}$ और $0$ जोड़ें.

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

चरण 5.2.20

$90 {(x^{3} - 2)}^{\frac{3}{5}}$ में से $180 {(x^{3} - 2)}^{\frac{3}{5}}$ घटाएं.

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

चरण 5.2.21

$270 {(x^{3} - 2)}^{\frac{2}{5}}$ में से $810 {(x^{3} - 2)}^{\frac{2}{5}}$ घटाएं.

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

चरण 5.2.22

$405 {(x^{3} - 2)}^{\frac{1}{5}}$ में से $1620 {(x^{3} - 2)}^{\frac{1}{5}}$ घटाएं.

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

चरण 5.2.23

जोड़कर और घटाकर सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.23.1

$241$ में से $1215$ घटाएं.

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

चरण 5.2.23.2

$- 974$ और $2430$ जोड़ें.

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

चरण 5.2.23.3

$1456$ में से $2430$ घटाएं.

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

चरण 5.2.23.4

$- 974$ और $1215$ जोड़ें.

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

चरण 5.2.23.5

$241$ में से $241$ घटाएं.

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

चरण 5.2.23.6

$x^{3}$ और $0$ जोड़ें.

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

चरण 5.2.24

$- 90 {(x^{3} - 2)}^{\frac{3}{5}}$ और $90 {(x^{3} - 2)}^{\frac{3}{5}}$ जोड़ें.

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

चरण 5.2.25

$x^{3}$ और $0$ जोड़ें.

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

चरण 5.2.26

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

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

चरण 5.2.27

$270 {(x^{3} - 2)}^{\frac{2}{5}}$ में से $270 {(x^{3} - 2)}^{\frac{2}{5}}$ घटाएं.

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

चरण 5.2.28

$x^{3}$ और $0$ जोड़ें.

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

चरण 5.2.29

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

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

चरण 5.2.30

$1215 {(x^{3} - 2)}^{\frac{1}{5}}$ में से $1620 {(x^{3} - 2)}^{\frac{1}{5}}$ घटाएं.

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

चरण 5.2.31

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

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

चरण 5.2.32

$x^{3}$ और $0$ जोड़ें.

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

चरण 5.2.33

वास्तविक संख्या मानकर, करणी के अंतर्गत से पदों को बाहर निकालें.

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

चरण 5.3

$f (f^{- 1} (x))$ का मान ज्ञात करें.

और स्टेप्स के लिए टैप करें…

चरण 5.3.1

समग्र परिणाम फलन सेट करें.

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

चरण 5.3.2

$f$ में $f^{- 1}$ का मान प्रतिस्थापित करके $f (\sqrt[3]{x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241})$ का मान ज्ञात करें.

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

चरण 5.3.3

प्रत्येक पद को सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 5.3.3.1

${\sqrt[3]{x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241}}^{3}$ को $x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241$ के रूप में फिर से लिखें.

और स्टेप्स के लिए टैप करें…

चरण 5.3.3.1.1

$\sqrt[3]{x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241}$ को ${(x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241)}^{\frac{1}{3}}$ के रूप में फिर से लिखने के लिए $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ का उपयोग करें.

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

चरण 5.3.3.1.2

घात नियम लागू करें और घातांक गुणा करें, ${(a^{m})}^{n} = a^{m n}$ .

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

चरण 5.3.3.1.3

$\frac{1}{3}$ और $3$ को मिलाएं.

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

चरण 5.3.3.1.4

$3$ का उभयनिष्ठ गुणनखंड रद्द करें.

और स्टेप्स के लिए टैप करें…

चरण 5.3.3.1.4.1

उभयनिष्ठ गुणनखंड रद्द करें.

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

चरण 5.3.3.1.4.2

व्यंजक को फिर से लिखें.

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

चरण 5.3.3.1.5

सरल करें.

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

चरण 5.3.3.2

$- 241$ में से $2$ घटाएं.

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

चरण 5.4

चूँकि $f^{- 1} (f (x)) = x$ और $f (f^{- 1} (x)) = x$ , तो $f^{- 1} (x) = \sqrt[3]{x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 241}$ , $f (x) = {(x^{3} - 2)}^{\frac{1}{5}} + 3$ का व्युत्क्रम है.

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