Precalculus Examples

$f (x) = \frac{1}{x - 5}$ , $g (x) = x^{2} + 2$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

$f (x^{2} + 2) = \frac{1}{(x^{2} + 2) - 5}$

Step 3

Subtract $5$ from $2$ .

$f (x^{2} + 2) = \frac{1}{x^{2} - 3}$