Why is not [-2,0] also in the range of along with [0,2]?

Hello!

When we define the square root function, the function which we start with is a square function   We want a function which, given an would return an such that   In other words, we want the inverse function for the square function.

But the problem is that the square function gives the same result(s) for and Therefore actually for any positive there are two roots: positive and negative. Usually we want that any function be one-valued (it is more convenient).

For this reason it was agreed between mathematicians that the symbol will denote the positive (non-negative) root, at least for real numbers. And in our example, is also non-negative for all 's for which it is defined This is the cause why isn't in the range of 

Note that the domain of this function does contain [-2,0) along with [0,2].