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Calculus Inverse Functions

  1. Apr 6, 2013 #1
    1. The problem statement, all variables and given/known data

    1. Show that the function f(x) = x5 -x3 +2x is invertible. Compute the derivative of f-1
    at 2.


    3. The attempt at a solution
    To find f-1 I switched x and y which gave me x = y5 - y3 + 2y

    this is where i got stuck because I am not sure how to solve for y after that step.

    Can the y5 - y3 become y2?

    Thanks
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 6, 2013 #2

    LCKurtz

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    Lucky for you, you weren't asked to calculate ##f^{-1}##, just show it exists. Can you show, for example, that ##f## is increasing?
    Of course not.
     
  4. Apr 7, 2013 #3

    joshmccraney

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    one really good way to see if numeric algebra works is to take a simple case and see what happens. what if [itex]y=1[/itex]?? then you know the answer to be zero yet if you adopt your proposition we see the answer is 1, which is of course incorrect.

    hope this helps for the future
     
  5. Apr 7, 2013 #4

    SammyS

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    What is necessary for a function to be invertible ?
     
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