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

Apr 15, 2016

#### Answer:

Domain: all Real values excluding $1$
Range: all Real values excluding $0$

#### Explanation:

Given $f \left(x\right) = \frac{1}{x - 1}$

Since division by $0$ is undefined
$\textcolor{w h i t e}{\text{XXX}} x - 1 \ne 0$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow x \ne 1$
However $f \left(x\right)$ is defined for all other values of $x$

Since $f \left(x\right) = \frac{1}{x - 1}$
then
$\textcolor{w h i t e}{\text{XXX}} \left(x - 1\right) \cdot f \left(x\right) = 1$
and the question of "Range" becomes
$\textcolor{w h i t e}{\text{XXX}}$for what value(s) of $f \left(x\right)$ is this not possible.
The only answer is that it is not possible if $f \left(x\right) = 0$.
So the Range is all Real values except $0$