# How do you find the domain and range of f(x) = (x+2) / (x-1)?

Apr 11, 2016

Domain and range $\left(- \infty , 1\right) U \left(1 , + \infty\right)$

#### Explanation:

To find the domain, it has to be seen whether f(x) exists for all values of x. If it does , its domain is all Real numbers. If it does not exists for some values of x. then those numbers are excluded from the domain.
In the present case f(x) would not exist for x=1, hence its domain would be all real numbers except 1. In set notation it would be written as $\left(- \infty , 1\right) U \left(1 , + \infty\right)$.

For range, write it as $y = \frac{x + 2}{x - 1}$. Interchange x and y and solve for y, as follows:

$x = \frac{y + 2}{y - 1} \Rightarrow y = \frac{x + 2}{x - 1}$ Now the domain of this function would be the range of the original function.

It so turns out that the domain of this function is also same, as that of the original function.

Hence range of original function would also be $\left(- \infty , 1\right) U \left(1 , + \infty\right)$