Question

How do you find the domain of `sqrt(x - 1)/(x + 4)`?

Answer 1

`[0, oo)`

Explanation:

The square root must be positive or zero, so

`x-1>=0 -> x>=1` is part of our domain.

However, we may not have division by zero either:

`x+4 ne 0`

`x ne -4`

From the first portion of the problem, where we ensure that we only have a positive root, `x=-4` is already excluded from the domain, so, this part of the problem only reinforces that `x>=0`.

The domain is then `[0, oo)`