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Math Help - Solving inverse function

  1. #1
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    Solving inverse function

    Hello I am having difficulty solving this question. Any help would be greatly appreciated.
    g(x)=3+x+e^x
    The e is the mathematical constant not a variable

    find g^{-1}(4)

    So I must find a value of x where g(x)=4

    this is my attempt:
    4=3+x+e^x
    1=x+e^x
    1-x=e^x
    I know that ln(e^x)=x so I thought of doing that
    ln(1-x)=x
    But I don't know what to do after that. Thanks for the assistance.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by iamanoobatmath View Post
    Hello I am having difficulty solving this question. Any help would be greatly appreciated.
    g(x)=3+x+e^x
    The e is the mathematical constant not a variable

    find g^{-1}(4)

    So I must find a value of x where g(x)=4

    this is my attempt:
    4=3+x+e^x
    1=x+e^x
    1-x=e^x
    I know that ln(e^x)=x so I thought of doing that
    ln(1-x)=x
    But I don't know what to do after that. Thanks for the assistance.
    At this stage, I can only complete it by observation:

    If x=0, then 1-0=e^0\implies 1=1

    So g^{-1}(4)=0
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  3. #3
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    Quote Originally Posted by Chris L T521 View Post
    At this stage, I can only complete it by observation:

    If x=0, then 1-0=e^0\implies 1=1

    So g^{-1}(4)=0
    Undoubtedly a solution by inspection was intended.
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