What is the domain and range of y=5/(x-1)?

Mar 5, 2018

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

Explanation:

$\text{the denominator of y cannot equal zero as this would }$
$\text{make y undefined. Equating the denominator to zero}$
$\text{and solving gives the value that x cannot be}$

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

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

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

$\Rightarrow y \left(x - 1\right) = 5$

$\Rightarrow x y - y = 5$

$\Rightarrow x y = 5 + y$

$\Rightarrow x = \frac{5 + y}{y}$

$\Rightarrow y = 0 \leftarrow \textcolor{red}{\text{excluded value}}$

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