Find g(h(x)) g(x)=15-4x h(x)=3/2x+8

$g (x) = 15 - 4 x$ $h (x) = \frac{3}{2} x + 8$

Set up the composite result function.

$g (h (x))$

Evaluate $g (\frac{3}{2} x + 8)$ by substituting in the value of $h$ into $g$ .

$g (\frac{3}{2} x + 8) = 15 - 4 (\frac{3}{2} x + 8)$

Simplify each term.

Combine $\frac{3}{2}$ and $x$ .

$g (\frac{3}{2} x + 8) = 15 - 4 (\frac{3 x}{2} + 8)$

Apply the distributive property.

$g (\frac{3}{2} x + 8) = 15 - 4 \frac{3 x}{2} - 4 \cdot 8$

Cancel the common factor of $2$ .

Factor $2$ out of $- 4$ .

$g (\frac{3}{2} x + 8) = 15 + 2 (- 2) (\frac{3 x}{2}) - 4 \cdot 8$

Cancel the common factor.

$g (\frac{3}{2} x + 8) = 15 + 2 \cdot (- 2 \frac{3 x}{2}) - 4 \cdot 8$

Rewrite the expression.

$g (\frac{3}{2} x + 8) = 15 - 2 (3 x) - 4 \cdot 8$

Multiply $3$ by $- 2$ .

$g (\frac{3}{2} x + 8) = 15 - 6 x - 4 \cdot 8$

Multiply $- 4$ by $8$ .

$g (\frac{3}{2} x + 8) = 15 - 6 x - 32$

Subtract $32$ from $15$ .

$g (\frac{3}{2} x + 8) = - 6 x - 17$