Page "Inverse function" Paragraph 14

If the domain is the real numbers, then each element in Y would correspond to two different elements in X (± x ), and therefore ƒ would not be invertible.

More precisely, the square of x is not invertible because it is impossible to deduce from its output the sign of its input.

Such a function is called non-injective or information-losing.

Notice that neither the square root nor the principal square root function is the inverse of x < sup > 2 </ sup > because the first is not single-valued, and the second returns-x when x is negative.