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Thread: 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 $\displaystyle y = 1 - \ln{(x - 2)}$.

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


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

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

    $\displaystyle y - 2 = e^{1 - x}$

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


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