Explain how to find reasonable domain values for a function

A reasonable domain and range is the set of values that exist for the function. The sets that are not reasonable are not considered domain and range. For instance, f(x) = 15√(x - 3) 
The reasonable domain is {x | R, x ≥ 3} since you can't have negative value inside the radicand. 
The reasonable range is {f(x) | R, f(x) ≥ 0} since the minimum value is 0 [Noting that x = 3 gives f(3) = 15√(3 - 3) = 15√0 = 0]