Definition:Inverse Hyperbolic Tangent/Real/Definition 1

Definition
Let $\tanh: \R \to S$ denote the hyperbolic tangent as defined on the set of real numbers, where $S$ is the closed interval $S := \left[{-1 \,.\,.\, 1}\right]$.

The inverse hyperbolic tangent is defined as:


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

Also see

 * Definition:Real Inverse Hyperbolic Sine
 * Definition:Real Inverse Hyperbolic Cosine
 * Definition:Real Inverse Hyperbolic Cotangent
 * Definition:Real Inverse Hyperbolic Secant
 * Definition:Real Inverse Hyperbolic Cosecant