Find g(f(x)) f(x)=8x+5 , g(x)=7x+1

$f (x) = 8 x + 5$ , $g (x) = 7 x + 1$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (8 x + 5)$ by substituting in the value of $f$ into $g$ .

$g (8 x + 5) = 7 (8 x + 5) + 1$

Step 3

Simplify each term.

Apply the distributive property.

$g (8 x + 5) = 7 (8 x) + 7 \cdot 5 + 1$

Multiply $8$ by $7$ .

$g (8 x + 5) = 56 x + 7 \cdot 5 + 1$

Multiply $7$ by $5$ .

$g (8 x + 5) = 56 x + 35 + 1$

Step 4

Add $35$ and $1$ .

$g (8 x + 5) = 56 x + 36$