Definition:Inverse Hyperbolic Cosine/Real

Definition
Let $S$ denote the subset of the real numbers:
 * $S = \set {x \in \R: x \ge 1}$

Definition 2
Hence for $x > 1$, $\map {\cosh^{-1} } x$ has $2$ values.

For $x < 1$, $\map {\cosh^{-1} } x$ is not defined.

Also see

 * Equivalence of Definitions of Real Area Hyperbolic Cosine


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