# What is the range of the function f(x)=1/(x+3)?

Jun 7, 2018

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

#### Explanation:

Let $y = \frac{1}{x + 3}$

$\implies$, $y \left(x + 3\right) = 1$

$\implies$, $y x + 3 y = 1$

$\implies$, $y x = 1 - 3 y$

$\implies$, $x = \frac{1 - 3 y}{y}$

The denominator $\ne 0$

$y \ne 0$

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

graph{1/(x+3) [-10, 10, -5, 5]}