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.
I know that it isn't one-to-one, I was just trying to apply the formal procedure outlined in my text.
Now that I think about it, the absolute value does break it since it makes different signed values for a and b equal even if they're not (such as your example). Thanks.