# What is the domain and range of 1/(x+2)?

Nov 24, 2017

$x \in \mathbb{R} , x \ne - 2$
$y \in \mathbb{R} , y \ne 0$

#### Explanation:

$\text{let } y = \frac{1}{x + 2}$

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

$\text{solve "x+2=0rArrx=-2larrcolor(red)"excluded value}$

$\Rightarrow \text{domain is } x \in \mathbb{R} , x \ne - 2$

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

$\Rightarrow y \left(x + 2\right) = 1$

$\Rightarrow x y + 2 y = 1$

$\Rightarrow x y = 1 - 2 y$

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

$\text{the denominator cannot be zero}$

$\Rightarrow \text{range is } y \in \mathbb{R} , y \ne 0$