Find f(g(x)) f(x)=-6x+9 , g(x)=7x+9

$f (x) = - 6 x + 9$ , $g (x) = 7 x + 9$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (7 x + 9)$ by substituting in the value of $g$ into $f$ .

$f (7 x + 9) = - 6 (7 x + 9) + 9$

Step 3

Simplify each term.

Apply the distributive property.

$f (7 x + 9) = - 6 (7 x) - 6 \cdot 9 + 9$

Multiply $7$ by $- 6$ .

$f (7 x + 9) = - 42 x - 6 \cdot 9 + 9$

Multiply $- 6$ by $9$ .

$f (7 x + 9) = - 42 x - 54 + 9$

Step 4

Add $- 54$ and $9$ .

$f (7 x + 9) = - 42 x - 45$