Definition:Inverse Hyperbolic Cotangent/Real/Definition 1

Definition
Let $\coth: \R \to S$ denote the hyperbolic cotangent as defined on the set of real numbers, where $S$ is the union of the unbounded closed intervals:
 * $S := \left({-\infty \,.\,.\, -1}\right] \cup \left[{1 \,.\,.\, +\infty}\right)$

The inverse hyperbolic cotangent defined as:


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

Also see

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