Algebra Examples

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

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

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

$g (4 x - 4) = \frac{1}{4} \cdot (4 x - 4) + 4$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$g (4 x - 4) = \frac{1}{4} \cdot (4 x) + \frac{1}{4} \cdot - 4 + 4$

Step 3.2

Cancel the common factor of $4$ .

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Step 3.2.1

Factor $4$ out of $4 x$ .

$g (4 x - 4) = \frac{1}{4} \cdot (4 (x)) + \frac{1}{4} \cdot - 4 + 4$

Step 3.2.2

Cancel the common factor.

$g (4 x - 4) = \frac{1}{4} \cdot (4 x) + \frac{1}{4} \cdot - 4 + 4$

Step 3.2.3

Rewrite the expression.

$g (4 x - 4) = x + \frac{1}{4} \cdot - 4 + 4$

Step 3.3

Cancel the common factor of $4$ .

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Step 3.3.1

Factor $4$ out of $- 4$ .

$g (4 x - 4) = x + \frac{1}{4} \cdot (4 (- 1)) + 4$

Step 3.3.2

Cancel the common factor.

$g (4 x - 4) = x + \frac{1}{4} \cdot (4 \cdot - 1) + 4$

Step 3.3.3

Rewrite the expression.

$g (4 x - 4) = x - 1 + 4$

Step 4

Add $- 1$ and $4$ .

$g (4 x - 4) = x + 3$