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Quick hyperbolic query

  1. Jun 9, 2005 #1
    This isn't exactly homework but I thought it was too basic to justify putting this post in the general math section.
    My question is: why is arcoshx defined as: arcoshx=ln[x+rt(x^2-1)] and not +-ln[x+rt(x^2-1)] ?
    Is it simply to keep it as a one to one function? I know that to have an inverse a function should be one to one but why is it not allowed for an inverse function to be 1 to 2 mapping?
    Last edited: Jun 9, 2005
  2. jcsd
  3. Jun 9, 2005 #2
    yeah, it'd be so that the inverse is a function.

    in what class/context did you come across this? if you're comfortable with functions of a complex variable, i'd say that it's because you have to specify a particular branch-cut in order for a function to be...nice.

    really, with just plain vanilla arccos x, we start off by restricting the domain of cosine, then finding the inverse function of it.

    so you can think of the same being done to coshx.
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