# What is the domain and range of g(x)= 2/ (x-1)?

Aug 11, 2015

Domain: $\left(- \infty , 1\right) \cup \left(1 , + \infty\right)$
Range: $\left(- \infty , 0\right) \cup \left(0 , + \infty\right)$

#### Explanation:

The domain of the function will be restricted by the fact that the denominator cannot be equal to zero.

$x - 1 \ne 0 \implies x \ne 1$

The domain will thus be $\mathbb{R} - \left\{1\right\}$, or $\left(- \infty , 1\right) \cup \left(1 , + \infty\right)$.

The range of the function will be restricted by the fact that this expression cannot be equal to zero, since the numerator is a constant.

The range of the function will thus be $\mathbb{R} - \left\{0\right\}$, or $\left(- \infty , 0\right) \cup \left(0 , + \infty\right)$.

graph{2/(x-1) [-7.9, 7.9, -3.95, 3.95]}