Find g(f(x)) f(x)=-10x+15 g(x)=5x+9

$f (x) = - 10 x + 15$ $g (x) = 5 x + 9$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (- 10 x + 15)$ by substituting in the value of $f$ into $g$ .

$g (- 10 x + 15) = 5 (- 10 x + 15) + 9$

Step 3

Simplify each term.

Apply the distributive property.

$g (- 10 x + 15) = 5 (- 10 x) + 5 \cdot 15 + 9$

Multiply $- 10$ by $5$ .

$g (- 10 x + 15) = - 50 x + 5 \cdot 15 + 9$

Multiply $5$ by $15$ .

$g (- 10 x + 15) = - 50 x + 75 + 9$

Step 4

Add $75$ and $9$ .

$g (- 10 x + 15) = - 50 x + 84$