Precalculus Examples

$f (x) = 4 x^{\frac{2}{3}}$

Step 1

Find $f (- x)$ .

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Step 1.1

Find $f (- x)$ by substituting $- x$ for all occurrence of $x$ in $f (x)$ .

$f (- x) = 4 {(- x)}^{\frac{2}{3}}$

Step 1.2

Simplify the expression.

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Step 1.2.1

Apply the product rule to $- x$ .

$f (- x) = 4 ({(- 1)}^{\frac{2}{3}} x^{\frac{2}{3}})$

Step 1.2.2

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$f (- x) = 4 ({({(- 1)}^{3})}^{\frac{2}{3}} x^{\frac{2}{3}})$

Step 1.2.3

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$f (- x) = 4 ({(- 1)}^{3 (\frac{2}{3})} x^{\frac{2}{3}})$

Step 1.3

Cancel the common factor of $3$ .

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Step 1.3.1

Cancel the common factor.

$f (- x) = 4 ({(- 1)}^{3 (\frac{2}{3})} x^{\frac{2}{3}})$

Step 1.3.2

Rewrite the expression.

$f (- x) = 4 ({(- 1)}^{2} x^{\frac{2}{3}})$

Step 1.4

Simplify the expression.

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Step 1.4.1

Raise $- 1$ to the power of $2$ .

$f (- x) = 4 (1 x^{\frac{2}{3}})$

Step 1.4.2

Multiply $x^{\frac{2}{3}}$ by $1$ .

$f (- x) = 4 x^{\frac{2}{3}}$

Step 2

A function is even if $f (- x) = f (x)$ .

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Step 2.1

Check if $f (- x) = f (x)$ .

Step 2.2

Since $4 x^{\frac{2}{3}} = 4 x^{\frac{2}{3}}$ , the function is even.

The function is even

Step 3