Question

How do you find the domain of `f(x) = 1/(sqrt(5 - x) - 1)`?

Answer 1

The domain, in this case. is all real numbers except for the values of `x` that would result in a non-real value.

Explanation:

If `x` causes the denominator to be `0`, then the function would be undefined at that point.

`0 = sqrt(5 - x) - 1`

`1 = sqrt(5 - x)`

`1^2 = 5 - x`

`1 = 5 - x`

`-4 = -x`

`x = 4`

The function would also be imaginary at `x` if there was a square root of a negative value. Therefore...

`sqrt(5 - x) >= 0`

`5 - x >= 0^2`

`5 >= x`

The domain of `x` is all real values less than or equal to `5` and not including `4`.