# What is the domain and range of f(x) = 4 / (x+2)?

May 16, 2018

The domain is $x \in \left(- \infty , - 2\right) \cup \left(- 2 , + \infty\right)$. The range is $y \in \left(- \infty , 0\right) \cup \left(0 , + \infty\right)$.

#### Explanation:

The denominator must be $\ne 0$

$x + 2 \ne 0$

Therefore,

$x \ne - 2$

The domain is $x \in \left(- \infty , - 2\right) \cup \left(- 2 , + \infty\right)$

To find the range, procceed as follow.

Let $y = \frac{4}{x + 2}$

$\implies$, $y \left(x + 2\right) = 4$

$\implies$, $y x + 2 y = 4$

$\implies$, $y x = 4 - 2 y$

$\implies$, $x = \frac{4 - 2 y}{y}$

The denominator must be $\ne 0$

$y \ne 0$

The range is $y \in \left(- \infty , 0\right) \cup \left(0 , + \infty\right)$

graph{4/(x+2) [-32.48, 32.48, -16.24, 16.24]}