Question

How do you find the domain and range of `sqrt(x - 1)`?

Answer 1

You can get the domain by working with the assumption that the function's domain lie in a set of all real numbers, that is `(x - 1)` must be greater than or equal to zero.

Explanation:

If `(x - 1)` must be greater than `0` then `x >= 1` must be true for all values of `x`.

Therefore the domain is `x >= 1`

The range is suppose to be the set of all values of the function that lies within the domain.
The least member of the domain set above is `x = 1` and the value of the function at this value of `x` is `√1` which is `1`.
Therefore the range is `{1, ...}`