Precalculus Examples

$g (x) = 3 x + 4$ $h (x) = 3 x - 1$ Find $g (h (x))$

Step 1

Set up the composite result function.

$g (h (x))$

Step 2

Evaluate $g (3 x - 1)$ by substituting in the value of $h$ into $g$ .

$g (3 x - 1) = 3 (3 x - 1) + 4$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$g (3 x - 1) = 3 (3 x) + 3 \cdot - 1 + 4$

Step 3.2

Multiply $3$ by $3$ .

$g (3 x - 1) = 9 x + 3 \cdot - 1 + 4$

Step 3.3

Multiply $3$ by $- 1$ .

$g (3 x - 1) = 9 x - 3 + 4$

Step 4

Add $- 3$ and $4$ .

$g (3 x - 1) = 9 x + 1$