Find f(g(x)) f(x)=-5x+14 g(x)=x^2+6x-7

$f (x) = - 5 x + 14$ $g (x) = x^{2} + 6 x - 7$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (x^{2} + 6 x - 7)$ by substituting in the value of $g$ into $f$ .

$f (x^{2} + 6 x - 7) = - 5 (x^{2} + 6 x - 7) + 14$

Step 3

Simplify each term.

Apply the distributive property.

$f (x^{2} + 6 x - 7) = - 5 x^{2} - 5 (6 x) - 5 \cdot - 7 + 14$

Simplify.

Multiply $6$ by $- 5$ .

$f (x^{2} + 6 x - 7) = - 5 x^{2} - 30 x - 5 \cdot - 7 + 14$

Multiply $- 5$ by $- 7$ .

$f (x^{2} + 6 x - 7) = - 5 x^{2} - 30 x + 35 + 14$

Step 4

Add $35$ and $14$ .

$f (x^{2} + 6 x - 7) = - 5 x^{2} - 30 x + 49$