\begin{definition}[Definition:Real Inverse Hyperbolic Function]
Let $f: \R \to \R$ be one of the hyperbolic functions on the set of real numbers.
Certain of the '''inverse hyperbolic function''' $f^{-1} \subseteq \R \times \R$ are actually multifunctions, such that for a given $y \in \R$ there may be more than one $x \in \R$ such that $y = \map f x$.
As with the inverse trigonometric functions, it is usual to restrict the codomain of the multifunction so as to allow $f^{-1}$ to be single-valued. 
There are six basic hyperbolic functions, so each of these has its inverse functions:
\end{definition}