Inverse Hyperbolic Functions

In this post we discuss about inverse Hyperbolic Function and also their domain and Range. The Inverse Hyperbolic Functions are expressed in terms of natural ;logarithms. 

Function    Formulas
Sinh-1x ln(x+\sqrt{x^2+1}), \forall \,\,\ x
Cosh-1x  ln(x+\sqrt{x^2-1}), \forall \,\,\ x\geq 1
Tanh-1x  \frac{1}{2}ln(\frac{1+x}{1-x}) , |x| < 1
Cosech-1x  ln(\frac{1}{x}+\frac{\sqrt{1+x^2}}{|x|}) , x \neq 0
Sech-1x  ln(\frac{1}{x}+\frac{\sqrt{1-x^2}}{|x|}) , 0 < x \leq 1
Coth-1x  \frac{1}{2}ln(\frac{x+1}{x-1}) , |x| < 1

 

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