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

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (2 x - 6)$ by substituting in the value of $g$ into $f$ .

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

Step 3

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $- 4$ .

$f (2 x - 6) = - 8 x - 4 \cdot - 6 + 7$

Multiply $- 4$ by $- 6$ .

$f (2 x - 6) = - 8 x + 24 + 7$

Step 4

Add $24$ and $7$ .

$f (2 x - 6) = - 8 x + 31$