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Math Help - [SOLVED] Inverse Function

  1. #1
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    [SOLVED] Inverse Function

    I would like to find the inverse function of  f(x)=x^3+3^x

    Since a^b = \exp{b\ln{a}}

     y=x^3+\exp{x\ln{3}}

    I do not know how to solve for x in terms of y.
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  2. #2
    Super Member General's Avatar
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    You can not solve it for x in terms of y by using the standard methods.
    Do you post all informations of this problem?
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  3. #3
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    Quote Originally Posted by Paperwings View Post
    I would like to find the inverse function of  f(x)=x^3+3^x

    Since a^b = \exp{b\ln{a}}

     y=x^3+\exp{x\ln{3}}

    I do not know how to solve for x in terms of y.
    Quite simply, you don't- not in terms of elementary functions.
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  4. #4
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    Quote Originally Posted by Paperwings View Post
    I would like to find the inverse function of  f(x)=x^3+3^x

    Since a^b = \exp{b\ln{a}}

     y=x^3+\exp{x\ln{3}}

    I do not know how to solve for x in terms of y.
    why do you need the inverse of this function?

    is there more top this problem than what you have stated?
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  5. #5
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    Let  f(x)=x^3+3^x. show that f has an inverse and find  (f^{-1})'{(4)}.

     (f^{-1})'{(c)} = \frac{1}{f'(a)}.

    If f(a) = 4, then a = 1. Since  f'(x)=3x^2+3^x\ln{3}, f'(1)=3+3ln3

    Thus,

     (f^{-1})'{(4)} = \frac{1}{f'(1)} = \frac{1}{3(1+\ln{3})} .

    I was just curious to see what the inverse of f was. I assume that to show that f has an inverse means to solve for the inverse. Since this function is an increasing function, it has an inverse.
    Last edited by Paperwings; January 14th 2010 at 08:05 AM.
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  6. #6
    Super Member General's Avatar
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    Quote Originally Posted by Paperwings View Post
     f^{-1}{(4)} = \frac{1}{f'(1)} .
    This is wrong.
    I think you mean the DERIVATIVE of the inverse function at 4 not just the value of the inverse function at 4.
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  7. #7
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    Quote Originally Posted by General View Post
    This is wrong.
    I think you mean the DERIVATIVE of the inverse function at 4 not just the value of the inverse function at 4.
    Yes, you are correct. I was fixing some Latex syntax errors, and forgot to put the derivative sign. Edit: Fixed it.
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  8. #8
    MHF Contributor Calculus26's Avatar
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    Since f(1) = 4

    f^(-1)(4) = 1


    f^(-1) ' (4) = 1/ f '(1) = 1/[3+3ln(2)]
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