Algebra Examples

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

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (- 2 x + 12)$ by substituting in the value of $f$ into $g$ .

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

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

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

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

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

Step 3.2.2

Factor $2$ out of $- 2 x$ .

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

Step 3.2.3

Cancel the common factor.

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

Step 3.2.4

Rewrite the expression.

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

Step 3.3

Multiply $- 1$ by $- 1$ .

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

Step 3.4

Multiply $x$ by $1$ .

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

Step 3.5

Cancel the common factor of $2$ .

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Step 3.5.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

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

Step 3.5.2

Factor $2$ out of $12$ .

$g (- 2 x + 12) = x + \frac{- 1}{2} \cdot (2 (6)) - 12$

Step 3.5.3

Cancel the common factor.

$g (- 2 x + 12) = x + \frac{- 1}{2} \cdot (2 \cdot 6) - 12$

Step 3.5.4

Rewrite the expression.

$g (- 2 x + 12) = x - 1 \cdot 6 - 12$

Step 3.6

Multiply $- 1$ by $6$ .

$g (- 2 x + 12) = x - 6 - 12$

Step 4

Subtract $12$ from $- 6$ .

$g (- 2 x + 12) = x - 18$