Algebra Examples

$f (x) = \frac{1}{x}$ , $g (x) = \frac{x - 4}{5}$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (\frac{1}{x})$ by substituting in the value of $f$ into $g$ .

$g (\frac{1}{x}) = \frac{(\frac{1}{x}) - 4}{5}$

Step 3

Simplify the numerator.

Tap for more steps...

Step 3.1

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$g (\frac{1}{x}) = \frac{\frac{1}{x} - 4 \cdot \frac{x}{x}}{5}$

Step 3.2

Combine $- 4$ and $\frac{x}{x}$ .

$g (\frac{1}{x}) = \frac{\frac{1}{x} + \frac{- 4 x}{x}}{5}$

Step 3.3

Combine the numerators over the common denominator.

$g (\frac{1}{x}) = \frac{\frac{1 - 4 x}{x}}{5}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$g (\frac{1}{x}) = \frac{1 - 4 x}{x} \cdot \frac{1}{5}$

Step 5

Multiply $\frac{1 - 4 x}{x}$ by $\frac{1}{5}$ .

$g (\frac{1}{x}) = \frac{1 - 4 x}{x \cdot 5}$

Step 6

Move $5$ to the left of $x$ .

$g (\frac{1}{x}) = \frac{1 - 4 x}{5 x}$