Inverse hyperbolic sine function

This article is about a particular function from a subset of the real numbers to the real numbers. Information about the function, including its domain, range, and key data relating to graphing, differentiation, and integration, is presented in the article.
View a complete list of particular functions on this wiki

Definition

The inverse hyperbolic sine function, denoted ${\sinh }^{-1}$, is defined in the following equivalent ways:

1. It is the inverse function to the hyperbolic sine function, i.e., ${\sinh }^{-1}x$ is defined as the unique real number $y$ such that $\sinh y=x$.
2. It is given explicitly by the expression:

${\sinh }^{-1}x:=\ln |x+\sqrt{x^2+1}|$