Definition:Inverse Hyperbolic Cosine/Real/Definition 2

Definition
The inverse hyperbolic cosine $\cosh^{-1}: \R \to \R$ on the set of real numbers is a real function defined as:


 * $\forall x \in \R_{\ge 1}: \cosh^{-1} \left({x}\right) := \ln \left({x + \sqrt{x^2 - 1} }\right)$

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 sine function is also known as the hyperbolic arcsine function.

Also see

 * Equivalence of Definitions of Real Inverse Hyperbolic Cosine