Definition:Inverse Hyperbolic Cosine/Real/Definition 2

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

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


 * $\forall x \in S: \map {\cosh^{-1} } x := \map \ln {x + \sqrt {x^2 - 1} }$

where:
 * $\sqrt {x^2 - 1}$ denotes the positive square root of $x^2 - 1$
 * $\ln$ denotes the natural logarithm of a (strictly positive) real number.

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