Find g(f(x)) f(x)=3x^2+6x+10 g(x)=2x-13

$f (x) = 3 x^{2} + 6 x + 10$ $g (x) = 2 x - 13$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (3 x^{2} + 6 x + 10)$ by substituting in the value of $f$ into $g$ .

$g (3 x^{2} + 6 x + 10) = 2 (3 x^{2} + 6 x + 10) - 13$

Step 3

Simplify each term.

Apply the distributive property.

$g (3 x^{2} + 6 x + 10) = 2 (3 x^{2}) + 2 (6 x) + 2 \cdot 10 - 13$

Simplify.

Multiply $3$ by $2$ .

$g (3 x^{2} + 6 x + 10) = 6 x^{2} + 2 (6 x) + 2 \cdot 10 - 13$

Multiply $6$ by $2$ .

$g (3 x^{2} + 6 x + 10) = 6 x^{2} + 12 x + 2 \cdot 10 - 13$

Multiply $2$ by $10$ .

$g (3 x^{2} + 6 x + 10) = 6 x^{2} + 12 x + 20 - 13$

Step 4

Subtract $13$ from $20$ .

$g (3 x^{2} + 6 x + 10) = 6 x^{2} + 12 x + 7$