Find F(g(x)) F(x)=3x+10 g(x)=x-2

$F (x) = 3 x + 10$ $g (x) = x - 2$

Set up the composite result function.

$F (g (x))$

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

$F (x - 2) = 3 (x - 2) + 10$

Simplify each term.

Apply the distributive property.

$F (x - 2) = 3 x + 3 \cdot - 2 + 10$

Multiply $3$ by $- 2$ .

$F (x - 2) = 3 x - 6 + 10$

Add $- 6$ and $10$ .

$F (x - 2) = 3 x + 4$