As noted by Feynman (1997), the notation is unfortunate because it conflicts with the common
interpretation of a superscripted quantity as indicating a power,
It is therefore important to keep in mind that the symbols , , etc., refer to the inverse
sine, inverse cosine, etc., and not
admits an inverse function (i.e., " is invertible") iff
it is bijective. However, inverse functions are commonly
defined for elementary functions that are multivalued
in the complex plane. In such cases, the inverse
relation holds on some subset of the complex plane but, over the whole plane, either
or both parts of the identity may fail to hold. A few examples
are illustrated above and in the following table. In the table and .
An additional counterintuitive property of inverse functions is that
so the expected identity does not hold along the negative real axis.