Find g(f(x)) f(x)=2x+5 , g(x)=3x-6

$f (x) = 2 x + 5$ , $g (x) = 3 x - 6$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (2 x + 5)$ by substituting in the value of $f$ into $g$ .

$g (2 x + 5) = 3 (2 x + 5) - 6$

Step 3

Simplify each term.

Apply the distributive property.

$g (2 x + 5) = 3 (2 x) + 3 \cdot 5 - 6$

Multiply $2$ by $3$ .

$g (2 x + 5) = 6 x + 3 \cdot 5 - 6$

Multiply $3$ by $5$ .

$g (2 x + 5) = 6 x + 15 - 6$

Step 4

Subtract $6$ from $15$ .

$g (2 x + 5) = 6 x + 9$