Algebra Examples

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

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Step 3.1

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

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Step 3.1.1

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

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

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $4$ out of $4$ .

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

Step 3.1.2.2

Cancel the common factor.

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

Step 3.1.2.3

Rewrite the expression.

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

Step 3.1.2.4

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

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

Step 3.2

Apply the distributive property.

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

Step 3.3

Multiply $- 1$ by $- 11$ .

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

Step 3.4

Apply the distributive property.

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

Step 3.5

Multiply $- - x$ .

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Step 3.5.1

Multiply $- 1$ by $- 1$ .

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

Step 3.5.2

Multiply $x$ by $1$ .

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

Step 3.6

Multiply $- 1$ by $11$ .

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

Step 4

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

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Step 4.1

Subtract $11$ from $11$ .

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

Step 4.2

Add $x$ and $0$ .

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