# Category:Definitions/Inverse Hyperbolic Functions

This category contains definitions related to Inverse Hyperbolic Functions.

Related results can be found in **Category:Inverse Hyperbolic Functions**.

### Complex Inverse Hyperbolic Function

Let $h: \C \to \C$ be one of the hyperbolic functions on the set of complex numbers.

The **inverse hyperbolic function** $h^{-1} \subseteq \C \times \C$ is actually a multifunction, as in general for a given $y \in \C$ there is more than one $x \in \C$ such that $y = \map h x$.

As with the inverse trigonometric functions, it is usual to restrict the codomain of the multifunction so as to allow $h^{-1}$ to be single-valued.

### Real Inverse Hyperbolic Function

Let $f: \R \to \R$ be one of the hyperbolic functions on the set of real numbers.

Certain of the **inverse hyperbolic function** $f^{-1} \subseteq \R \times \R$ are actually multifunctions, such that for a given $y \in \R$ there may be more than one $x \in \R$ such that $y = \map f x$.

As with the inverse trigonometric functions, it is usual to restrict the codomain of the multifunction so as to allow $f^{-1}$ to be single-valued.

## Subcategories

This category has the following 6 subcategories, out of 6 total.

## Pages in category "Definitions/Inverse Hyperbolic Functions"

The following 14 pages are in this category, out of 14 total.

### I

- Definition:Inverse Hyperbolic Cosecant
- Definition:Inverse Hyperbolic Cosine
- Definition:Inverse Hyperbolic Cotangent
- Definition:Inverse Hyperbolic Function
- Definition:Inverse Hyperbolic Function/Also known as
- Definition:Inverse Hyperbolic Function/Notation
- Definition:Inverse Hyperbolic Secant
- Definition:Inverse Hyperbolic Sine
- Definition:Inverse Hyperbolic Tangent