Definition:Inverse Hyperbolic Tangent/Real/Definition 1

Definition
Let $S$ denote the closed real interval:
 * $S := \left[{-1 \,.\,.\, 1}\right]$

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


 * $\forall x \in S: \tanh^{-1} \left({x}\right) := y \in \R: x = \tanh \left({y}\right)$

where $\tanh \left({y}\right)$ denotes the hyperbolic tangent function.

Also known as
The inverse hyperbolic tangent function is also known as the hyperbolic arctangent function.

Also see

 * Equivalence of Definitions of Real Inverse Hyperbolic Tangent