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Math Help - What's the inverse of g(x) = 3 + x + e^x

  1. #1
    TGS
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    What's the inverse of g(x) = 3 + x + e^x

    g(x) = 3 + x + e^x

    Help please?
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  2. #2
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    Quote Originally Posted by TGS View Post
    g(x) = 3 + x + e^x

    Help please?
    is this the original question, or did it arise from working out something else?
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  3. #3
    TGS
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    its the original question, but i just solved it so nevermind.

    Thanks though.
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  4. #4
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    Quote Originally Posted by TGS View Post
    its the original question, but i just solved it so nevermind.

    Thanks though.
    is that so ? I would love to see how you found g^{-1}(x).
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  5. #5
    Senior Member bkarpuz's Avatar
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    Quote Originally Posted by skeeter View Post
    is that so ? I would love to see how you found g^{-1}(x).
    me too
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  6. #6
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    y=3+x+e^{x}

    e^{y-3}=e^{x+e^x}

    Now putting it in standard Lambert-W terms:

    e^{y-3}=e^x e^{e^x}

    so:

    e^x=W(e^{y-3})

    but:

    y-3-x=e^{x}

    then:

    x=y-3-W(e^{y-3})

    . . . end special function discrimination. Equal rights for special functions.
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  7. #7
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    I was hoping for a non-Lambert W function algebraic miracle.
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  8. #8
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    Can someone please provide a simple method to determine this answer? I don't recall how to deal with two variables in an inverse situation especially with one as an exponent. Thanks!
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  9. #9
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    Quote Originally Posted by Atinus View Post
    Can someone please provide a simple method to determine this answer? I don't recall how to deal with two variables in an inverse situation especially with one as an exponent. Thanks!
    If you read this thread while awake you would realise that a 'simple method' is not possible (unless you consider using the Lambert W-function simple).
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