Find f(g(x)) f(x)=-2x-7 , g(x)=-4x+3

$f (x) = - 2 x - 7$ , $g (x) = - 4 x + 3$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (- 4 x + 3)$ by substituting in the value of $g$ into $f$ .

$f (- 4 x + 3) = - 2 (- 4 x + 3) - 7$

Step 3

Simplify each term.

Apply the distributive property.

$f (- 4 x + 3) = - 2 (- 4 x) - 2 \cdot 3 - 7$

Multiply $- 4$ by $- 2$ .

$f (- 4 x + 3) = 8 x - 2 \cdot 3 - 7$

Multiply $- 2$ by $3$ .

$f (- 4 x + 3) = 8 x - 6 - 7$

Step 4

Subtract $7$ from $- 6$ .

$f (- 4 x + 3) = 8 x - 13$