Question

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

Answer 1

The domain is: `D=RR-{-6}` 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=RR-{-6}`

or as the sum of 2 intervals:

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