Algebra Examples

$f (x) = - 2 x + 12$ , $g (x) = - \frac{1}{2} x - 12$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (- \frac{1}{2} x - 12)$ by substituting in the value of $g$ into $f$ .

$f (- \frac{1}{2} x - 12) = - 2 (- \frac{1}{2} x - 12) + 12$

Step 3

Simplify each term.

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Step 3.1

Combine $x$ and $\frac{1}{2}$ .

$f (- \frac{1}{2} x - 12) = - 2 (- \frac{x}{2} - 12) + 12$

Step 3.2

Apply the distributive property.

$f (- \frac{1}{2} x - 12) = - 2 (- \frac{x}{2}) - 2 \cdot - 12 + 12$

Step 3.3

Cancel the common factor of $2$ .

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Step 3.3.1

Move the leading negative in $- \frac{x}{2}$ into the numerator.

$f (- \frac{1}{2} x - 12) = - 2 \frac{- x}{2} - 2 \cdot - 12 + 12$

Step 3.3.2

Factor $2$ out of $- 2$ .

$f (- \frac{1}{2} x - 12) = 2 (- 1) (\frac{- x}{2}) - 2 \cdot - 12 + 12$

Step 3.3.3

Cancel the common factor.

$f (- \frac{1}{2} x - 12) = 2 \cdot (- 1 \frac{- x}{2}) - 2 \cdot - 12 + 12$

Step 3.3.4

Rewrite the expression.

$f (- \frac{1}{2} x - 12) = - 1 (- x) - 2 \cdot - 12 + 12$

Step 3.4

Multiply $- 1$ by $- 1$ .

$f (- \frac{1}{2} x - 12) = 1 x - 2 \cdot - 12 + 12$

Step 3.5

Multiply $x$ by $1$ .

$f (- \frac{1}{2} x - 12) = x - 2 \cdot - 12 + 12$

Step 3.6

Multiply $- 2$ by $- 12$ .

$f (- \frac{1}{2} x - 12) = x + 24 + 12$

Step 4

Add $24$ and $12$ .

$f (- \frac{1}{2} x - 12) = x + 36$