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Math Help - inverse function of natural log?

  1. #1
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    inverse function of natural log?

    For the problem f(x) = 1 - ln(x - 2) how would I find the inverse (f^-1) ? And how would I confirm that algebraically?


    Thanks.
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  2. #2
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    You have y = 1 - \ln{(x - 2)}.

    To find the inverse function, swap your x and y values...


    x = 1 - \ln{(y - 2)}

    \ln{(y - 2)} = 1 - x

    y - 2 = e^{1 - x}

    y = 2 + e^{1 - x}.


    So f^{-1}(x) = 2 + e^{1 - x}.
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