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Inverse functions

  1. Nov 12, 2008 #1

    jgens

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    Does anyone know of an existing methodology for determining and proving whether or not a function has an inverse?

    Thanks.
     
  2. jcsd
  3. Nov 13, 2008 #2

    nicksauce

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    How about by determining if the function is a bijection? Or am I missing something here?
     
  4. Nov 13, 2008 #3

    HallsofIvy

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    The "horizontal line test". How many times does any horizontal line cross the graph of the function? Which is the same as "determining if the function is a bijection"!
     
  5. Nov 13, 2008 #4

    jgens

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    Thank you very much. Just a brief follow up question: Suppose a function is invertable but the inverse has no representation in terms of elementary functions (I'm including trigonometric and logarithmic functions in this category) - I think f(x) = x + sin(x) would meet this criterion - is there a general method for proving that the function does not have an inverse expressable in terms of elementary functions?

    Sorry if that doesn't make sense.
     
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