Find f(g(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.

$f (g (x))$

Step 2

Evaluate $f (2 x - 4)$ by substituting in the value of $g$ into $f$ .

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

Step 3

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $9$ .

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

Multiply $9$ by $- 4$ .

$f (2 x - 4) = 18 x - 36 - 2$

Step 4

Subtract $2$ from $- 36$ .

$f (2 x - 4) = 18 x - 38$