Precalculus Examples

If $f (x) = \frac{1}{x}$ and $g (x) = 3 x + 2$ find $((g \circ f)) (x)$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (\frac{1}{x})$ by substituting in the value of $f$ into $g$ .

$g (\frac{1}{x}) = 3 (\frac{1}{x}) + 2$

Step 3

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

$g (\frac{1}{x}) = \frac{3}{x} + 2$