Find g(f(x)) f(x)=6x-6 , g(x)=7-3x

$f (x) = 6 x - 6$ , $g (x) = 7 - 3 x$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

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

$g (6 x - 6) = 7 - 3 (6 x - 6)$

Step 3

Simplify each term.

Apply the distributive property.

$g (6 x - 6) = 7 - 3 (6 x) - 3 \cdot - 6$

Multiply $6$ by $- 3$ .

$g (6 x - 6) = 7 - 18 x - 3 \cdot - 6$

Multiply $- 3$ by $- 6$ .

$g (6 x - 6) = 7 - 18 x + 18$

Step 4

Add $7$ and $18$ .

$g (6 x - 6) = - 18 x + 25$