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Math Help - Finding the inverse function of a logarithm

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    Finding the inverse function of a logarithm

    f= ln(2x-1) Find the inverse function stating its domain.
    Last edited by mr fantastic; November 24th 2008 at 03:50 AM. Reason: Deleted first question after copying thread to pre-calc forum
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  2. #2
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    Quote Originally Posted by brooksy View Post
    f= ln(2x-1) Find the inverse function stating its domain.
    1. You have:

    f: y = \ln(2x-1) , domain D=\left(\frac12\ ,\ \infty\right) and range R=\mathbb{R}

    2. Then the inverse function is:

    f^{-1}:x=\ln(2y-1)\ ,\ D_{f^{-1}}=\mathbb{R}\ and\ R_{f^{-1}}= \left(\frac12\ ,\ \infty\right)

    That means:

    x=\ln(2y-1)~\implies~e^x=2y-1~\implies~\boxed{y=\dfrac{e^x+1}{2}}
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    thanks.
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