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Math Help - definition of arccosh

  1. #1
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    definition of arccosh

    Hi, does anyone know how to do this? I am really stuck on this . Thanks a lot!

    "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.)
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  2. #2
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    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.
    Last edited by croraf; October 28th 2010 at 01:16 PM.
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  3. #3
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    Quote Originally Posted by juanma101285 View Post
    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
    \text{arccosh} (z) = \log \left[ {z + \left( {z^2  - 1} \right)^{\frac{1}{2}} } \right]
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