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

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

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

Step 3

Simplify each term.

Apply the distributive property.

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

Simplify.

Multiply $2$ by $- 1$ .

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

Multiply $- 3$ by $- 1$ .

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

Multiply $- 1$ by $- 7$ .

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

Step 4

Add $7$ and $3$ .

$f (2 x^{2} - 3 x - 7) = - 2 x^{2} + 3 x + 10$