Originally Posted by

**Glitch** **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:

$\displaystyle a^2 = b^2$

$\displaystyle \sqrt{a^2} = \sqrt{b^2}$

$\displaystyle |a| = |b|$

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.