Find f(g(x)) f(x)=-2x+4 , g(x)=6x+7

$f (x) = - 2 x + 4$ , $g (x) = 6 x + 7$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (6 x + 7)$ by substituting in the value of $g$ into $f$ .

$f (6 x + 7) = - 2 (6 x + 7) + 4$

Step 3

Simplify each term.

Apply the distributive property.

$f (6 x + 7) = - 2 (6 x) - 2 \cdot 7 + 4$

Multiply $6$ by $- 2$ .

$f (6 x + 7) = - 12 x - 2 \cdot 7 + 4$

Multiply $- 2$ by $7$ .

$f (6 x + 7) = - 12 x - 14 + 4$

Step 4

Add $- 14$ and $4$ .

$f (6 x + 7) = - 12 x - 10$