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

Apr 3, 2017

see explanation.

#### Explanation:

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be.

$x + 2 = 0 \to x = - 2$

$\text{domain is } x \in \mathbb{R} , x \ne - 2$

Rearrange the function expressing x in terms of y

$\Rightarrow y = \frac{x - 1}{x + 2}$

$\Rightarrow y \left(x + 2\right) - x + 1 = 0$

$\Rightarrow x y + 2 y - x + 1 = 0$

$\Rightarrow x \left(y - 1\right) = - 2 y - 1$

$\Rightarrow x = - \frac{2 y + 1}{y - 1}$

$\text{range is } y \in \mathbb{R} , y \ne 1$