Algebra Examples

$f (x) = - \frac{1}{4} x - 2$ $g (x) = x - 7$

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 $f$ .

$f (x - 7) = - \frac{1}{4} \cdot (x - 7) - 2$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$f (x - 7) = - \frac{1}{4} x - \frac{1}{4} \cdot - 7 - 2$

Step 3.2

Combine $x$ and $\frac{1}{4}$ .

$f (x - 7) = - \frac{x}{4} - \frac{1}{4} \cdot - 7 - 2$

Step 3.3

Multiply $- \frac{1}{4} \cdot - 7$ .

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Step 3.3.1

Multiply $- 7$ by $- 1$ .

$f (x - 7) = - \frac{x}{4} + 7 (\frac{1}{4}) - 2$

Step 3.3.2

Combine $7$ and $\frac{1}{4}$ .

$f (x - 7) = - \frac{x}{4} + \frac{7}{4} - 2$

Step 4

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$f (x - 7) = - \frac{x}{4} + \frac{7}{4} - 2 \cdot \frac{4}{4}$

Step 5

Combine $- 2$ and $\frac{4}{4}$ .

$f (x - 7) = - \frac{x}{4} + \frac{7}{4} + \frac{- 2 \cdot 4}{4}$

Step 6

Combine the numerators over the common denominator.

$f (x - 7) = - \frac{x}{4} + \frac{7 - 2 \cdot 4}{4}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $- 2$ by $4$ .

$f (x - 7) = - \frac{x}{4} + \frac{7 - 8}{4}$

Step 7.2

Subtract $8$ from $7$ .

$f (x - 7) = - \frac{x}{4} + \frac{- 1}{4}$

Step 8

Move the negative in front of the fraction.

$f (x - 7) = - \frac{x}{4} - \frac{1}{4}$