Definition:Inverse Hyperbolic Secant/Real/Definition 1

Definition
Let $S$ denote the half-open real interval:
 * $S := \hointl 0 1$

The inverse hyperbolic secant $\sech^{-1}: S \to \R$ is a real function defined on $S$ as:


 * $\forall x \in S: \map {\sech^{-1} } x := y \in \R_{\ge 0}: x = \map \sech y$

where $\map \sech y$ denotes the hyperbolic secant function.

Hence for $0 < x < 1$, $\map {\sech^{-1} } x$ has $2$ values.

For $x > 0$ and $x > 1$, $\map {\sech^{-1} } x$ is not defined.

Also see

 * Equivalence of Definitions of Real Area Hyperbolic Secant