I do this:

f(x) = x^2

y = x^2

x = y^2

root(x) = y Since for some y in Z there is not an x in Z, this function does not map Z onto Z.

Am I thinking about this right? I am guessing no because isn't there some theorem that states that the set of natural numbers and the set of its squares are bijective? Doesn't this say that maps N to N? No real difference between N and Z. I need some clarification here. Thanks.