The question:

Show that the function f: R -> R, given by f(x) = x^2, is not one-to-one.

My attempt:

According to my text, "A function f is said to be one-to-one if f(a) = f(b) implies that a = b whenever a, b is an element Dom(f).

So:

I know by intuition that x^2 is not one to one, however it appears that a does equal b. Or is the fact that each side is the absolute value that the proof fails? Thank you.