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

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

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (5 x - 2)$ by substituting in the value of $f$ into $g$ .

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

Step 3

Simplify each term.

Apply the distributive property.

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

Multiply $5$ by $2$ .

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

Multiply $2$ by $- 2$ .

$g (5 x - 2) = 10 x - 4 + 1$

Step 4

Add $- 4$ and $1$ .

$g (5 x - 2) = 10 x - 3$