Definition:Inverse Hyperbolic Cosine/Real/Definition 1

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

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


 * $\forall x \in S: \cosh^{-1} \left({x}\right) := y \in \R_{\ge 0}: x = \cosh \left({y}\right)$

where $\cosh \left({y}\right)$ denotes the hyperbolic cosine function.

Also known as
The inverse hyperbolic cosine function is also known as the hyperbolic arccosine function.

Also see

 * Equivalence of Definitions of Real Inverse Hyperbolic Cosine