Algebra Examples

$f (x) = 4 x - 16$ , $g (x) = \frac{x}{4} + 4$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (4 x - 16)$ by substituting in the value of $f$ into $g$ .

$g (4 x - 16) = \frac{4 x - 16}{4} + 4$

Step 3

Cancel the common factor of $4 x - 16$ and $4$ .

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Step 3.1

Factor $4$ out of $4 x$ .

$g (4 x - 16) = \frac{4 (x) - 16}{4} + 4$

Step 3.2

Factor $4$ out of $- 16$ .

$g (4 x - 16) = \frac{4 (x) + 4 \cdot - 4}{4} + 4$

Step 3.3

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

$g (4 x - 16) = \frac{4 (x - 4)}{4} + 4$

Step 3.4

Cancel the common factors.

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Step 3.4.1

Factor $4$ out of $4$ .

$g (4 x - 16) = \frac{4 (x - 4)}{4 (1)} + 4$

Step 3.4.2

Cancel the common factor.

$g (4 x - 16) = \frac{4 (x - 4)}{4 \cdot 1} + 4$

Step 3.4.3

Rewrite the expression.

$g (4 x - 16) = \frac{x - 4}{1} + 4$

Step 3.4.4

Divide $x - 4$ by $1$ .

$g (4 x - 16) = x - 4 + 4$

Step 4

Combine the opposite terms in $x - 4 + 4$ .

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Step 4.1

Add $- 4$ and $4$ .

$g (4 x - 16) = x + 0$

Step 4.2

Add $x$ and $0$ .

$g (4 x - 16) = x$