Find f(g(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.

$f (g (x))$

Step 2

Evaluate $f (7 x + 1)$ by substituting in the value of $g$ into $f$ .

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

Step 3

Simplify each term.

Apply the distributive property.

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

Multiply $7$ by $8$ .

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

Multiply $8$ by $1$ .

$f (7 x + 1) = 56 x + 8 + 5$

Step 4

Add $8$ and $5$ .

$f (7 x + 1) = 56 x + 13$