Find f(g(x)) f(x)=5x+8 g(x)=x^2+7x-2

$f (x) = 5 x + 8$ $g (x) = x^{2} + 7 x - 2$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

$f (x^{2} + 7 x - 2) = 5 (x^{2} + 7 x - 2) + 8$

Step 3

Simplify each term.

Apply the distributive property.

$f (x^{2} + 7 x - 2) = 5 x^{2} + 5 (7 x) + 5 \cdot - 2 + 8$

Simplify.

Multiply $7$ by $5$ .

$f (x^{2} + 7 x - 2) = 5 x^{2} + 35 x + 5 \cdot - 2 + 8$

Multiply $5$ by $- 2$ .

$f (x^{2} + 7 x - 2) = 5 x^{2} + 35 x - 10 + 8$

Step 4

Add $- 10$ and $8$ .

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