Precalculus Examples

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

Step 1

Set up the composite result function.

$h (g (x))$

Step 2

Evaluate $h (4 x + 3)$ by substituting in the value of $g$ into $h$ .

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

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

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

Step 3.2

Multiply $4$ by $- 3$ .

$h (4 x + 3) = - 12 x - 3 \cdot 3 + 1$

Step 3.3

Multiply $- 3$ by $3$ .

$h (4 x + 3) = - 12 x - 9 + 1$

Step 4

Add $- 9$ and $1$ .

$h (4 x + 3) = - 12 x - 8$