Algebra Examples

$f (x) = 2 x - 6$ , $g (x) = \frac{x + 6}{2}$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (2 x - 6)$ by substituting in the value of $f$ into $g$ .

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

Step 3

Cancel the common factor of $(2 x - 6) + 6$ and $2$ .

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Step 3.1

Factor $2$ out of $2 x$ .

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

Step 3.2

Factor $2$ out of $- 6$ .

$g (2 x - 6) = \frac{2 (x) + 2 \cdot - 3 + 6}{2}$

Step 3.3

Factor $2$ out of $2 (x) + 2 (- 3)$ .

$g (2 x - 6) = \frac{2 (x - 3) + 6}{2}$

Step 3.4

Factor $2$ out of $6$ .

$g (2 x - 6) = \frac{2 (x - 3) + 2 \cdot 3}{2}$

Step 3.5

Factor $2$ out of $2 (x - 3) + 2 (3)$ .

$g (2 x - 6) = \frac{2 (x - 3 + 3)}{2}$

Step 3.6

Cancel the common factors.

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Step 3.6.1

Factor $2$ out of $2$ .

$g (2 x - 6) = \frac{2 (x - 3 + 3)}{2 (1)}$

Step 3.6.2

Cancel the common factor.

$g (2 x - 6) = \frac{2 (x - 3 + 3)}{2 \cdot 1}$

Step 3.6.3

Rewrite the expression.

$g (2 x - 6) = \frac{x - 3 + 3}{1}$

Step 3.6.4

Divide $x - 3 + 3$ by $1$ .

$g (2 x - 6) = x - 3 + 3$

Step 4

Combine the opposite terms in $x - 3 + 3$ .

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Step 4.1

Add $- 3$ and $3$ .

$g (2 x - 6) = x + 0$

Step 4.2

Add $x$ and $0$ .

$g (2 x - 6) = x$