Find g(f(x)) f(x)=3x^2+4x-7 g(x)=2x-11

$f (x) = 3 x^{2} + 4 x - 7$ $g (x) = 2 x - 11$

Set up the composite result function.

$g (f (x))$

Evaluate $g (3 x^{2} + 4 x - 7)$ by substituting in the value of $f$ into $g$ .

$g (3 x^{2} + 4 x - 7) = 2 (3 x^{2} + 4 x - 7) - 11$

Simplify each term.

Apply the distributive property.

$g (3 x^{2} + 4 x - 7) = 2 (3 x^{2}) + 2 (4 x) + 2 \cdot - 7 - 11$

Simplify.

Multiply $3$ by $2$ .

$g (3 x^{2} + 4 x - 7) = 6 x^{2} + 2 (4 x) + 2 \cdot - 7 - 11$

Multiply $4$ by $2$ .

$g (3 x^{2} + 4 x - 7) = 6 x^{2} + 8 x + 2 \cdot - 7 - 11$

Multiply $2$ by $- 7$ .

$g (3 x^{2} + 4 x - 7) = 6 x^{2} + 8 x - 14 - 11$

Subtract $11$ from $- 14$ .

$g (3 x^{2} + 4 x - 7) = 6 x^{2} + 8 x - 25$