Find g(f(x)) f(x)=3x-5 , g(x)=2x+1

$f (x) = 3 x - 5$ , $g (x) = 2 x + 1$

Set up the composite result function.

$g (f (x))$

Evaluate $g (3 x - 5)$ by substituting in the value of $f$ into $g$ .

$g (3 x - 5) = 2 (3 x - 5) + 1$

Simplify each term.

Apply the distributive property.

$g (3 x - 5) = 2 (3 x) + 2 \cdot - 5 + 1$

Multiply $3$ by $2$ .

$g (3 x - 5) = 6 x + 2 \cdot - 5 + 1$

Multiply $2$ by $- 5$ .

$g (3 x - 5) = 6 x - 10 + 1$

Add $- 10$ and $1$ .

$g (3 x - 5) = 6 x - 9$