Find g(f(x)) f(x)=3x^2+5x+15 g(x)=-3x+13

$f (x) = 3 x^{2} + 5 x + 15$ $g (x) = - 3 x + 13$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (3 x^{2} + 5 x + 15)$ by substituting in the value of $f$ into $g$ .

$g (3 x^{2} + 5 x + 15) = - 3 (3 x^{2} + 5 x + 15) + 13$

Step 3

Simplify each term.

Apply the distributive property.

$g (3 x^{2} + 5 x + 15) = - 3 (3 x^{2}) - 3 (5 x) - 3 \cdot 15 + 13$

Simplify.

Multiply $3$ by $- 3$ .

$g (3 x^{2} + 5 x + 15) = - 9 x^{2} - 3 (5 x) - 3 \cdot 15 + 13$

Multiply $5$ by $- 3$ .

$g (3 x^{2} + 5 x + 15) = - 9 x^{2} - 15 x - 3 \cdot 15 + 13$

Multiply $- 3$ by $15$ .

$g (3 x^{2} + 5 x + 15) = - 9 x^{2} - 15 x - 45 + 13$

Step 4

Add $- 45$ and $13$ .

$g (3 x^{2} + 5 x + 15) = - 9 x^{2} - 15 x - 32$