# How do you find the domain and range of y = { 1/ (x - 1) }?

Oct 26, 2017

$x \in \mathbb{R} , x \ne 1 , y \in \mathbb{R} , y \ne 0$

#### Explanation:

The denominator of y cannot be zero as this would make y undefined. Equating the denominator to zero and solving gives the value that x cannot be.

$\text{solve "x-1=0rArrx=1larrcolor(red)" excluded value}$

$\Rightarrow \text{domain is } x \in \mathbb{R} , x \ne 1$

$\text{for the range, rearrange making x the subject}$

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

$\Rightarrow x y - y = 1$

$\Rightarrow x y = 1 + y$

$\Rightarrow x = \frac{1 + y}{y}$

$\text{the denominator } \ne 0$

$\Rightarrow \text{range is } y \in \mathbb{R} , y \ne 0$
graph{1/(x-1) [-10, 10, -5, 5]}