Inverse hyperbolic functions
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Inverse Hyperbolic Functions
To have an inverse a function must be one-one. sinh x sinh x is a one-one function and consequently has an inverse, sinh-1 x, (also denoted as arcsinh x) defined on the whole of [Equation goes here - download the original to see it.] [Diagram goes here - download the original to see it. cosh x cosh x is not a one-one function. Consequently, in order to define its inverse we must restrict its domain to a part where it is one-one. For this purpose we chose that part of the domain where x is positive [Equation goes here - download the original to see it.] On this region, which we call the principal value, cosh x is increasing and hence has an inverse [Equation goes here - download the original to see it.] [Diagram goes here - download the original to see it.] tanh x tanh x in an always increasing, one-one function, and has an inverse defined on its entire domain. [Diagram goes here - download the original to see it.]
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Contents of
Inverse hyperbolic functions
1 Inverse Hyperbolic Functions
2 The Logarithmic forms of the inverse hyperbolic functions
3 Derivatives of the inverse hyperbolic functions
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