Find g(f(x)) f(x)=2x-5 , g(x)=4x+3

$f (x) = 2 x - 5$ , $g (x) = 4 x + 3$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

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

$g (2 x - 5) = 4 (2 x - 5) + 3$

Step 3

Simplify each term.

Apply the distributive property.

$g (2 x - 5) = 4 (2 x) + 4 \cdot - 5 + 3$

Multiply $2$ by $4$ .

$g (2 x - 5) = 8 x + 4 \cdot - 5 + 3$

Multiply $4$ by $- 5$ .

$g (2 x - 5) = 8 x - 20 + 3$

Step 4

Add $- 20$ and $3$ .

$g (2 x - 5) = 8 x - 17$