# How do you find the domain of 1/(x+6)?

Jul 13, 2016

The domain is: $D = \mathbb{R} - \left\{- 6\right\}$ or D=(-oo;-6)uu(-6;+oo)

#### Explanation:

To find the domain of a function you have to think about all values of $x$ for which the function's formula makes sense. In the example above only limitation is that $0$ cannot be the value of the denominator, so to find out which point is excluded from the domain you have to solve the equation $x + 6 = 0$

This equation has one solution $x = - 6$, so the domain of the function is the set of all real numbers except number $- 6$. We can write it in two ways:

$D = \mathbb{R} - \left\{- 6\right\}$

or as the sum of 2 intervals:

D=(-oo;-6)uu(-6;+oo)