Definition:Inverse Hyperbolic Tangent/Real/Definition 1

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Let $S$ denote the open 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