Find g(f(x)) f(x)=2x+8 , g(x)=5x-6

$f (x) = 2 x + 8$ , $g (x) = 5 x - 6$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (2 x + 8)$ by substituting in the value of $f$ into $g$ .

$g (2 x + 8) = 5 (2 x + 8) - 6$

Step 3

Simplify each term.

Apply the distributive property.

$g (2 x + 8) = 5 (2 x) + 5 \cdot 8 - 6$

Multiply $2$ by $5$ .

$g (2 x + 8) = 10 x + 5 \cdot 8 - 6$

Multiply $5$ by $8$ .

$g (2 x + 8) = 10 x + 40 - 6$

Step 4

Subtract $6$ from $40$ .

$g (2 x + 8) = 10 x + 34$