Hey Elusive1324.

There is no difference between |x|^2 and x^2 in terms of the map. In other words for the same values of x you get the same y for both functions. If you really want to prove it then break up the |x| into negative and positive x and show that the relationship holds since you get analytic functions (-x for x < 0 and x for x >= 0) which can be compared.