Find g(f(x)) f(x)=2x-6 , g(x)=2x+5

$f (x) = 2 x - 6$ , $g (x) = 2 x + 5$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (2 x - 6)$ by substituting in the value of $f$ into $g$ .

$g (2 x - 6) = 2 (2 x - 6) + 5$

Step 3

Simplify each term.

Apply the distributive property.

$g (2 x - 6) = 2 (2 x) + 2 \cdot - 6 + 5$

Multiply $2$ by $2$ .

$g (2 x - 6) = 4 x + 2 \cdot - 6 + 5$

Multiply $2$ by $- 6$ .

$g (2 x - 6) = 4 x - 12 + 5$

Step 4

Add $- 12$ and $5$ .

$g (2 x - 6) = 4 x - 7$