# What is the range of the function f(x) =1 / x?

Nov 26, 2017

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

#### Explanation:

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

$\text{express the function with x as the subject}$

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

$\text{the denominator cannot be zero as this would make}$
$\text{x undefined}$

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

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