Algebra Examples

$\sqrt[3]{3 x}$

Step 1

Write $\sqrt[3]{3 x}$ as a function.

$f (x) = \sqrt[3]{3 x}$

Step 2

Find $f (- x)$ .

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

$f (- x) = \sqrt[3]{3 (- x)}$

Multiply $- 1$ by $3$ .

$f (- x) = \sqrt[3]{- 3 x}$

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

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Rewrite $- 3$ as $- 1 (3)$ .

$f (- x) = \sqrt[3]{- 1 \cdot 3 x}$

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

$f (- x) = \sqrt[3]{{(- 1)}^{3} \cdot (3 x)}$

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

$f (- x) = \sqrt[3]{{({(- 1)}^{3})}^{3} \cdot (3 x)}$

Add parentheses.

$f (- x) = \sqrt[3]{{({(- 1)}^{3})}^{3} \cdot (3 x)}$

Pull terms out from under the radical.

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

Simplify the expression.

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Raise $- 1$ to the power of $3$ .

$f (- x) = - 1 \sqrt[3]{3 x}$

Rewrite $- 1 \sqrt[3]{3 x}$ as $- \sqrt[3]{3 x}$ .

$f (- x) = - \sqrt[3]{3 x}$

Step 3

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

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

$- \sqrt[3]{3 x}$ $\neq$ $\sqrt[3]{3 x}$

Since $- \sqrt[3]{3 x}$ $\neq$ $\sqrt[3]{3 x}$ , the function is not even.

The function is not even

Step 4

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

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Multiply $- 1$ by $\sqrt[3]{3 x}$ .

$- f (x) = - \sqrt[3]{3 x}$

Since $- \sqrt[3]{3 x} = - \sqrt[3]{3 x}$ , the function is odd.

The function is odd

Step 5