Algebra Examples

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

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (3 x - 1)$ by substituting in the value of $f$ into $g$ .

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

Step 3

Simplify the numerator.

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Step 3.1

Apply the distributive property.

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

Step 3.2

Multiply $3$ by $2$ .

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

Step 3.3

Multiply $2$ by $- 1$ .

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

Step 3.4

Subtract $1$ from $- 2$ .

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

Step 3.5

Factor $3$ out of $6 x - 3$ .

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Step 3.5.1

Factor $3$ out of $6 x$ .

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

Step 3.5.2

Factor $3$ out of $- 3$ .

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

Step 3.5.3

Factor $3$ out of $3 (2 x) + 3 (- 1)$ .

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