Algebra Examples

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

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (\frac{4}{x})$ by substituting in the value of $f$ into $g$ .

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

Step 3

Simplify the denominator.

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Step 3.1

Apply the product rule to $\frac{4}{x}$ .

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

Step 3.2

Raise $4$ to the power of $2$ .

$g (\frac{4}{x}) = \frac{4}{\frac{16}{x^{2}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$g (\frac{4}{x}) = 4 (\frac{x^{2}}{16})$

Step 5

Cancel the common factor of $4$ .

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Step 5.1

Factor $4$ out of $16$ .

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

Step 5.2

Cancel the common factor.

$g (\frac{4}{x}) = 4 (\frac{x^{2}}{4 \cdot 4})$

Step 5.3

Rewrite the expression.

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