Algebra Examples

$f (x) = 3 x - 4$ , $g (x) = \frac{1}{3} (x + 4)$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (3 x - 4)$ by substituting in the value of $f$ into $g$ .

$g (3 x - 4) = \frac{1}{3} \cdot ((3 x - 4) + 4)$

Step 3

Combine the opposite terms in $(3 x - 4) + 4$ .

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Step 3.1

Add $- 4$ and $4$ .

$g (3 x - 4) = \frac{1}{3} \cdot (3 x + 0)$

Step 3.2

Add $3 x$ and $0$ .

$g (3 x - 4) = \frac{1}{3} \cdot (3 x)$

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Factor $3$ out of $3 x$ .

$g (3 x - 4) = \frac{1}{3} \cdot (3 (x))$

Step 4.2

Cancel the common factor.

$g (3 x - 4) = \frac{1}{3} \cdot (3 x)$

Step 4.3

Rewrite the expression.

$g (3 x - 4) = x$