Find g(f(x)) f(x)=2x+1 g(x)=-5x+2

$f (x) = 2 x + 1$ $g (x) = - 5 x + 2$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (2 x + 1)$ by substituting in the value of $f$ into $g$ .

$g (2 x + 1) = - 5 (2 x + 1) + 2$

Step 3

Simplify each term.

Apply the distributive property.

$g (2 x + 1) = - 5 (2 x) - 5 \cdot 1 + 2$

Multiply $2$ by $- 5$ .

$g (2 x + 1) = - 10 x - 5 \cdot 1 + 2$

Multiply $- 5$ by $1$ .

$g (2 x + 1) = - 10 x - 5 + 2$

Step 4

Add $- 5$ and $2$ .

$g (2 x + 1) = - 10 x - 3$