Find g(f(x)) f(x)=6x+3 , g(x)=8x+6

$f (x) = 6 x + 3$ , $g (x) = 8 x + 6$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (6 x + 3)$ by substituting in the value of $f$ into $g$ .

$g (6 x + 3) = 8 (6 x + 3) + 6$

Step 3

Simplify each term.

Apply the distributive property.

$g (6 x + 3) = 8 (6 x) + 8 \cdot 3 + 6$

Multiply $6$ by $8$ .

$g (6 x + 3) = 48 x + 8 \cdot 3 + 6$

Multiply $8$ by $3$ .

$g (6 x + 3) = 48 x + 24 + 6$

Step 4

Add $24$ and $6$ .

$g (6 x + 3) = 48 x + 30$