function analysis question

[quinyu]

Given a function f(x), how do I find the domain and image/range of it? (The domain being the set of x values that the function can accept; and the range being the set of f(x) results that the function can have.)

For example, I have the function f(x)=ASIN(SQRT(x)), valid on reals. I know that it must have 0<=x<=1. I also know that (assuming you're working in radians) 0<=f(x)<=pi/2. How do you pull these results in the CAS in a symbolic form?

For the moment, let's not go into the ugly thicket of how to work it out on complex numbers. I know how to get the above results on an Nspire CAS, but couldn't for my life figure how it can be obtained on the HP Prime. Suggestions, please.