Definition:Inverse Hyperbolic Secant/Real/Definition 1

Definition
Let $\operatorname{sech}: \R \to S$ denote the hyperbolic secant as defined on the set of real numbers, where $S$ is the half-open interval $S := \left({0 \,.\,.\, 1}\right)$.

The inverse hyperbolic secant is a multifunction defined as:


 * $\forall x \in \R: \operatorname{sech}^{-1} \left({x}\right) = \left\{{y \in \R: x = \operatorname{sech} \left({y}\right)}\right\}$

Also see

 * Definition:Real Inverse Hyperbolic Sine
 * Definition:Real Inverse Hyperbolic Cosine
 * Definition:Real Inverse Hyperbolic Tangent
 * Definition:Real Inverse Hyperbolic Cotangent
 * Definition:Real Inverse Hyperbolic Cosecant