Find f(g(n)) f(n)=(-16+n)/4 , g(n)=4n+16

$f (n) = \frac{- 16 + n}{4}$ , $g (n) = 4 n + 16$

Step 1

Set up the composite result function.

$f (g (n))$

Step 2

Evaluate $f (4 n + 16)$ by substituting in the value of $g$ into $f$ .

$f (4 n + 16) = \frac{- 16 + 4 n + 16}{4}$

Step 3

Remove parentheses.

$f (4 n + 16) = \frac{- 16 + 4 n + 16}{4}$

Step 4

Cancel the common factor of $- 16 + 4 n + 16$ and $4$ .

Factor $4$ out of $- 16$ .

$f (4 n + 16) = \frac{4 \cdot - 4 + 4 n + 16}{4}$

Factor $4$ out of $4 n$ .

$f (4 n + 16) = \frac{4 \cdot - 4 + 4 (n) + 16}{4}$

Factor $4$ out of $16$ .

$f (4 n + 16) = \frac{4 \cdot - 4 + 4 (n) + 4 \cdot 4}{4}$

Factor $4$ out of $4 (n) + 4 (4)$ .

$f (4 n + 16) = \frac{4 \cdot - 4 + 4 (n + 4)}{4}$

Factor $4$ out of $4 (- 4) + 4 (n + 4)$ .

$f (4 n + 16) = \frac{4 (- 4 + n + 4)}{4}$

Cancel the common factors.

Factor $4$ out of $4$ .

$f (4 n + 16) = \frac{4 (- 4 + n + 4)}{4 (1)}$

Cancel the common factor.

$f (4 n + 16) = \frac{4 (- 4 + n + 4)}{4 \cdot 1}$

Rewrite the expression.

$f (4 n + 16) = \frac{- 4 + n + 4}{1}$

Divide $- 4 + n + 4$ by $1$ .

$f (4 n + 16) = - 4 + n + 4$

Step 5

Combine the opposite terms in $- 4 + n + 4$ .

Add $- 4$ and $4$ .

$f (4 n + 16) = n + 0$

Add $n$ and $0$ .

$f (4 n + 16) = n$