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For hyperbolic cosine, it is referred to as ( \text{arc}\cosh ) or ( \cosh^{-1} ).
For hyperbolic tangent, the symbol is ( \text{arc}\tanh ) or ( \tanh^{-1} ).
The fundamental property when dealing with these functions involves solving for ( y ) when ( x ) equals the hyperbolic function of ( y ). The relationship can be rewritten:
For ( \sinh(y) = x ), we rearrange to solve for ( y ).
Similarly, for ( \cosh(y) = x ) and ( \tanh(y) = x ), equations can be manipulated accordingly.
Graphical Representation of Hyperbolic Functions
Graphing hyperbolic functions assists in understanding their inverses, primarily because the requirement for a function to have an inverse is that it be one-to-one.