Find f(g(x)) f(x)=3x+5 g(x)=x-7

$f (x) = 3 x + 5$ $g (x) = x - 7$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

$f (x - 7) = 3 (x - 7) + 5$

Step 3

Simplify each term.

Apply the distributive property.

$f (x - 7) = 3 x + 3 \cdot - 7 + 5$

Multiply $3$ by $- 7$ .

$f (x - 7) = 3 x - 21 + 5$

Step 4

Add $- 21$ and $5$ .

$f (x - 7) = 3 x - 16$