Find f(g(x)) f(x)=3x+2 , g(x)=2x-3

$f (x) = 3 x + 2$ , $g (x) = 2 x - 3$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (2 x - 3)$ by substituting in the value of $g$ into $f$ .

$f (2 x - 3) = 3 (2 x - 3) + 2$

Step 3

Simplify each term.

Apply the distributive property.

$f (2 x - 3) = 3 (2 x) + 3 \cdot - 3 + 2$

Multiply $2$ by $3$ .

$f (2 x - 3) = 6 x + 3 \cdot - 3 + 2$

Multiply $3$ by $- 3$ .

$f (2 x - 3) = 6 x - 9 + 2$

Step 4

Add $- 9$ and $2$ .

$f (2 x - 3) = 6 x - 7$