Question

Question regarding function in discrete mathematics

Answer 1

√4 = 2, not -2.      That's why we sometimes write +/-√x  when we need to refer to +√x or -√x as part of a solution set.

Answer 2

Well, the radical  by definition only returns the positive square root, so that still defines a function.

If you wanted to have a relation between (x,y) where x = y^(2), then that would not be a function as (4,2) and (4,-2) would be in your relation, and that violates the second condition of being a function.

Not every relation is a function, in other words.