Find g(f(x)) f(x)=9x-2 , g(x)=2x-4

$f (x) = 9 x - 2$ , $g (x) = 2 x - 4$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (9 x - 2)$ by substituting in the value of $f$ into $g$ .

$g (9 x - 2) = 2 (9 x - 2) - 4$

Step 3

Simplify each term.

Apply the distributive property.

$g (9 x - 2) = 2 (9 x) + 2 \cdot - 2 - 4$

Multiply $9$ by $2$ .

$g (9 x - 2) = 18 x + 2 \cdot - 2 - 4$

Multiply $2$ by $- 2$ .

$g (9 x - 2) = 18 x - 4 - 4$

Step 4

Subtract $4$ from $- 4$ .

$g (9 x - 2) = 18 x - 8$