# How do you find the domain and range of f(x) = 2/(x-1)?

Sep 2, 2015

The domain is color(red)(x≠1); the range is color(red)(y≠0).

#### Explanation:

$f \left(x\right) = \frac{2}{x - 1}$

When $x = 1 , y = \frac{2}{0}$.

The value of $\frac{2}{0}$ is undefined, so $x$ cannot equal $1$.

The domain is x≠1.

As $x$ becomes large and positive, the value of $y$ approaches zero but never reaches it.

The same thing happens as $x$ becomes large and negative.

$y$ can have any value except zero.

The range is is y≠0.