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Math Help - Finding the Inverse Function

  1. #1
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    Finding the Inverse Function

    Given the function
    f(x) = 5x^3 + 4x - 4
    Let g be the inverse function of f. i.e. g(x)=f−1(x).
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  2. #2
    MHF Contributor Calculus26's Avatar
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    what is the entire pblm? In general it is very difficulat to solve a cubic equation see Cubic function - Wikipedia, the free encyclopedia


    I would be willing to bet to solve you're given pblm we may not need

    to solve for f^(-1)(x) in general
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  3. #3
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    its asking me to find the inverse of f(x) and then enter f(5) then do the same but with the derivative so f'(5)
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  4. #4
    MHF Contributor Calculus26's Avatar
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    If you want f ^(-1)(5)

    f(x) = 5x^3 + 4x -4

    note f(1) =5 so f^(-1)(5) = 1

    For the derivative [f^(-1)] ' (5) use the theorem on the derivative of the inverse:

    if f(a) = c

    Then [f^(-1)] ' (c) = 1/f '(a)

    In terms of g : g ' (c) =1/f '(a)

    In particular [f^(-1)] ' (5) = 1/f '(1) = 1/19
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  5. #5
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    Thanks I was really confused how to go about it.
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  6. #6
    Super Member bigwave's Avatar
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    Quote Originally Posted by Lolcats View Post
    its asking me to find the inverse of f(x) and then enter f(5) then do the same but with the derivative so f'(5)
    question was answered
    Last edited by bigwave; January 20th 2010 at 11:55 AM. Reason: already answered
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