Find f(h(x)) f(x)=11-x/4 and h(x)=-4(x-11)

$f (x) = 11 - \frac{x}{4}$ and $h (x) = - 4 (x - 11)$

Step 1

Set up the composite result function.

$f (h (x))$

Step 2

Evaluate $f (- 4 (x - 11))$ by substituting in the value of $h$ into $f$ .

$f (- 4 (x - 11)) = 11 - \frac{- 4 (x - 11)}{4}$

Step 3

Simplify each term.

Cancel the common factor of $- 4$ and $4$ .

Factor $4$ out of $- 4 (x - 11)$ .

$f (- 4 (x - 11)) = 11 - \frac{4 (- (x - 11))}{4}$

Cancel the common factors.

Factor $4$ out of $4$ .

$f (- 4 (x - 11)) = 11 - \frac{4 (- (x - 11))}{4 (1)}$

Cancel the common factor.

$f (- 4 (x - 11)) = 11 - \frac{4 (- (x - 11))}{4 \cdot 1}$

Rewrite the expression.

$f (- 4 (x - 11)) = 11 - \frac{- (x - 11)}{1}$

Divide $- (x - 11)$ by $1$ .

$f (- 4 (x - 11)) = 11 + x - 11$

Apply the distributive property.

$f (- 4 (x - 11)) = 11 - (- x + 11)$

Multiply $- 1$ by $- 11$ .

$f (- 4 (x - 11)) = 11 - (- x + 11)$

Apply the distributive property.

$f (- 4 (x - 11)) = 11 + x - 1 \cdot 11$

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

$f (- 4 (x - 11)) = 11 + 1 x - 1 \cdot 11$

Multiply $x$ by $1$ .

$f (- 4 (x - 11)) = 11 + x - 1 \cdot 11$

Multiply $- 1$ by $11$ .

$f (- 4 (x - 11)) = 11 + x - 11$

Step 4

Combine the opposite terms in $11 + x - 11$ .

Subtract $11$ from $11$ .

$f (- 4 (x - 11)) = x + 0$

Add $x$ and $0$ .

$f (- 4 (x - 11)) = x$