 Inverse hyperbolic functions

The inverse hyperbolic functions invert the hyperbolic functions, with real branches on their standard ranges and complex branches obtained through analytic continuation. For example, $\mathrm{arsinh}z=\log (z+\sqrt{z^2+1})$ on a chosen branch; the multivalued inverse hyperbolic sine records all inverse values.

Inverse hyperbolic functions are the inverse functions of the hyperbolic functions, similar to how the inverse trigonometric functions relate to trigonometric functions.