Find g(f(x)) f(x)=x^2-x+7 g(x)=-2x+14

$f (x) = x^{2} - x + 7$ $g (x) = - 2 x + 14$

Set up the composite result function.

$g (f (x))$

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

$g (x^{2} - x + 7) = - 2 (x^{2} - x + 7) + 14$

Simplify each term.

Apply the distributive property.

$g (x^{2} - x + 7) = - 2 x^{2} - 2 (- x) - 2 \cdot 7 + 14$

Simplify.

Multiply $- 1$ by $- 2$ .

$g (x^{2} - x + 7) = - 2 x^{2} + 2 x - 2 \cdot 7 + 14$

Multiply $- 2$ by $7$ .

$g (x^{2} - x + 7) = - 2 x^{2} + 2 x - 14 + 14$

Combine the opposite terms in $- 2 x^{2} + 2 x - 14 + 14$ .

Add $- 14$ and $14$ .

$g (x^{2} - x + 7) = - 2 x^{2} + 2 x + 0$

Add $- 2 x^{2} + 2 x$ and $0$ .

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