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.)