If f(x)=√x-a/√x-b is rational function.Then find the relation between a and b?

You need to learn proper presentation. I guess you meant f(x) = √(x - a)/√(x - b) but we are not supposed to have to guess.

A function defines a process with one output for each qualified input. "Range" means all possible outputs, and "domain" means all qualified inputs. It does not define any relationship between the inputs.