You can say that the arccosh is the inverse function of cosh therefore you can define it as cosh (arc cosh (x)) = x and arccosh (cosh (x)) = x, also you must check the domains.
Hi, does anyone know how to do this? I am really stuck on this : "Give a sensible definition of an arccosh function, analogous to the definitions of arcsin and arccos. (You are reminded that cosh x = (e^x+e^-x)/2.)
If this is a complex variables question, then
$\displaystyle \text{arccosh} (z) = \log \left[ {z + \left( {z^2 - 1} \right)^{\frac{1}{2}} } \right]$