Find f(g(x)) f(x)=-2x+5 , g(x)=5x+9

$f (x) = - 2 x + 5$ , $g (x) = 5 x + 9$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (5 x + 9)$ by substituting in the value of $g$ into $f$ .

$f (5 x + 9) = - 2 (5 x + 9) + 5$

Step 3

Simplify each term.

Apply the distributive property.

$f (5 x + 9) = - 2 (5 x) - 2 \cdot 9 + 5$

Multiply $5$ by $- 2$ .

$f (5 x + 9) = - 10 x - 2 \cdot 9 + 5$

Multiply $- 2$ by $9$ .

$f (5 x + 9) = - 10 x - 18 + 5$

Step 4

Add $- 18$ and $5$ .

$f (5 x + 9) = - 10 x - 13$