# How do you find the domain of g(x)= 1/x?

Mar 24, 2018

$\left\{x \in \mathbb{R} : x \ne 0\right\}$

$\left(- \infty , 0\right) \cup \left(0 , \infty\right)$

#### Explanation:

$g \left(x\right) = \frac{1}{x}$ is undefined for $x = 0$ ( division by zero )

It is defined for all $\mathbb{R}$ except $0$:

We can express this in set notation as:

$\left\{x \in \mathbb{R} : x \ne 0\right\}$

Or a union of intervals:

$\left(- \infty , 0\right) \cup \left(0 , \infty\right)$

The parenthesis indicate open intervals, end points not included.