A calculus of the absurd

15.2.2 Inverse functions

All the hyperbolic functions have inverses, although for some of them, it is necessary to restrict the domain.

As noted in the "functions" section (although I might not have uploaded that section yet?), functions can only have inverses if they are one-to-one (i.e. for every value the function outputs, there can only be one possible input which would have resulted in that output.) The graph of \(y=\cosh (x)\) is not one-to-one for the whole domain (some outputs correspond to multiple inputs), so we have to restrict its value.

The inverse functions are in the formula booklet of most maths exam boards. Otherwise, they can be derived.