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

Aug 16, 2017

Domain: $\left(- \infty , - 2\right) \cup \left(- 2 , + \infty\right)$
Range: $\left(- \infty , 0\right) \cup \left(0 , + \infty\right)$

#### Explanation:

f(x) = 1/(x+2

$f \left(x\right)$ is defined $\forall x \in \mathbb{R}$ except $x = - 2$

Hence, the domain of $f \left(x\right)$ in interval notation is$\left(- \infty , - 2\right) \cup \left(- 2 , + \infty\right)$

Consider ${\lim}_{x \to - 2 -} = - \infty$

And ${\lim}_{x \to - 2 +} = + \infty$

Also, $f \left(x\right) \ne 0$ for any finite $x$

Hence, the range of $f \left(x\right)$ is $\left(- \infty , 0\right) \cup \left(0 , + \infty\right)$

As can be seen by the graph of $f \left(x\right)$ below.

graph{1/(x+2) [-10, 10, -5, 5]}