Calculus Examples

$f (x) = \frac{8}{x}$ , $g (x) = 4 - x^{2}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (4 - x^{2})$ by substituting in the value of $g$ into $f$ .

$f (4 - x^{2}) = \frac{8}{4 - x^{2}}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $4$ as $2^{2}$ .

$f (4 - x^{2}) = \frac{8}{2^{2} - x^{2}}$

Step 3.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2$ and $b = x$ .

$f (4 - x^{2}) = \frac{8}{(2 + x) (2 - x)}$