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

Feb 25, 2017

The domain of $y$ is ${D}_{y} = \mathbb{R} - \left\{1\right\}$
The range of $y$ is ${R}_{y} = \mathbb{R} - \left\{0\right\}$

#### Explanation:

As you cannot divide by $0$, $x \ne 1$

The domain of $y$ is ${D}_{y} = \mathbb{R} - \left\{1\right\}$

To find the range, we need ${y}^{-} 1$

$y = \frac{2}{x - 1}$

$\left(x - 1\right) y = 2$

$x y - y = 2$

$x y = y + 2$

$x = \frac{y + 2}{y}$

Therefore,

${y}^{-} 1 = \frac{x + 2}{x}$

The domain of ${y}^{-} 1 = \mathbb{R} - \left\{0\right\}$

This is the range of $y$

The range of $y$ is ${R}_{y} = \mathbb{R} - \left\{0\right\}$