Find g(f(x)) f(x)=5x-2 , g(x)=6x+3

$f (x) = 5 x - 2$ , $g (x) = 6 x + 3$

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 $g$ .

$g (5 x - 2) = 6 (5 x - 2) + 3$

Step 3

Simplify each term.

Apply the distributive property.

$g (5 x - 2) = 6 (5 x) + 6 \cdot - 2 + 3$

Multiply $5$ by $6$ .

$g (5 x - 2) = 30 x + 6 \cdot - 2 + 3$

Multiply $6$ by $- 2$ .

$g (5 x - 2) = 30 x - 12 + 3$

Step 4

Add $- 12$ and $3$ .

$g (5 x - 2) = 30 x - 9$