Find g(f(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.

$g (f (x))$

Step 2

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

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

Step 3

Simplify each term.

Apply the distributive property.

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

Multiply $3$ by $2$ .

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

Multiply $2$ by $2$ .

$g (3 x + 2) = 6 x + 4 - 3$

Step 4

Subtract $3$ from $4$ .

$g (3 x + 2) = 6 x + 1$