Algebra Examples

$g (x) = {(2 x)}^{3}$ and $h (x) = \frac{\sqrt[3]{x}}{2}$

Step 1

Set up the composite result function.

$g (h (x))$

Step 2

Evaluate $g (\frac{\sqrt[3]{x}}{2})$ by substituting in the value of $h$ into $g$ .

$g (\frac{\sqrt[3]{x}}{2}) = {(2 (\frac{\sqrt[3]{x}}{2}))}^{3}$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Cancel the common factor.

$g (\frac{\sqrt[3]{x}}{2}) = {(2 (\frac{\sqrt[3]{x}}{2}))}^{3}$

Step 3.2

Rewrite the expression.

$g (\frac{\sqrt[3]{x}}{2}) = {\sqrt[3]{x}}^{3}$

Step 4

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

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Step 4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x}$ as $x^{\frac{1}{3}}$ .

$g (\frac{\sqrt[3]{x}}{2}) = {(x^{\frac{1}{3}})}^{3}$

Step 4.2

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

$g (\frac{\sqrt[3]{x}}{2}) = x^{\frac{1}{3} \cdot 3}$

Step 4.3

Combine $\frac{1}{3}$ and $3$ .

$g (\frac{\sqrt[3]{x}}{2}) = x^{\frac{3}{3}}$

Step 4.4

Cancel the common factor of $3$ .

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Step 4.4.1

Cancel the common factor.

$g (\frac{\sqrt[3]{x}}{2}) = x^{\frac{3}{3}}$

Step 4.4.2

Rewrite the expression.

$g (\frac{\sqrt[3]{x}}{2}) = x$

Step 4.5

Simplify.

$g (\frac{\sqrt[3]{x}}{2}) = x$