Find g(f(x)) f(x)=3x^2+6x-4 g(x)=-3x+4

$f (x) = 3 x^{2} + 6 x - 4$ $g (x) = - 3 x + 4$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (3 x^{2} + 6 x - 4)$ by substituting in the value of $f$ into $g$ .

$g (3 x^{2} + 6 x - 4) = - 3 (3 x^{2} + 6 x - 4) + 4$

Step 3

Simplify each term.

Apply the distributive property.

$g (3 x^{2} + 6 x - 4) = - 3 (3 x^{2}) - 3 (6 x) - 3 \cdot - 4 + 4$

Simplify.

Multiply $3$ by $- 3$ .

$g (3 x^{2} + 6 x - 4) = - 9 x^{2} - 3 (6 x) - 3 \cdot - 4 + 4$

Multiply $6$ by $- 3$ .

$g (3 x^{2} + 6 x - 4) = - 9 x^{2} - 18 x - 3 \cdot - 4 + 4$

Multiply $- 3$ by $- 4$ .

$g (3 x^{2} + 6 x - 4) = - 9 x^{2} - 18 x + 12 + 4$

Step 4

Add $12$ and $4$ .

$g (3 x^{2} + 6 x - 4) = - 9 x^{2} - 18 x + 16$