Algebra Examples

$f (x) = \frac{x^{3}}{27}$ and $h (x) = 27 \sqrt[3]{x}$

Step 1

Set up the composite result function.

$h (f (x))$

Step 2

Evaluate $h (\frac{x^{3}}{27})$ by substituting in the value of $f$ into $h$ .

$h (\frac{x^{3}}{27}) = 27 \sqrt[3]{\frac{x^{3}}{27}}$

Step 3

Remove parentheses.

$h (\frac{x^{3}}{27}) = 27 \sqrt[3]{\frac{x^{3}}{27}}$

Step 4

Rewrite $27$ as $3^{3}$ .

$h (\frac{x^{3}}{27}) = 27 \sqrt[3]{\frac{x^{3}}{3^{3}}}$

Step 5

Rewrite $\frac{x^{3}}{3^{3}}$ as ${(\frac{x}{3})}^{3}$ .

$h (\frac{x^{3}}{27}) = 27 \sqrt[3]{{(\frac{x}{3})}^{3}}$

Step 6

Pull terms out from under the radical, assuming real numbers.

$h (\frac{x^{3}}{27}) = 27 (\frac{x}{3})$

Step 7

Cancel the common factor of $3$ .

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Step 7.1

Factor $3$ out of $27$ .

$h (\frac{x^{3}}{27}) = 3 (9) (\frac{x}{3})$

Step 7.2

Cancel the common factor.

$h (\frac{x^{3}}{27}) = 3 \cdot (9 (\frac{x}{3}))$

Step 7.3

Rewrite the expression.

$h (\frac{x^{3}}{27}) = 9 x$