Find f(g(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.

$f (g (x))$

Step 2

Evaluate $f (7 - 3 x)$ by substituting in the value of $g$ into $f$ .

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

Step 3

Simplify each term.

Apply the distributive property.

$f (7 - 3 x) = 6 \cdot 7 + 6 (- 3 x) - 6$

Multiply $6$ by $7$ .

$f (7 - 3 x) = 42 + 6 (- 3 x) - 6$

Multiply $- 3$ by $6$ .

$f (7 - 3 x) = 42 - 18 x - 6$

Step 4

Subtract $6$ from $42$ .

$f (7 - 3 x) = - 18 x + 36$