Finding the inverse function of a logarithm

**brooksy** · November 24th 2008, 03:40 AM

f= ln(2x-1) Find the inverse function stating its domain.

**earboth** · November 24th 2008, 04:41 AM

Originally Posted by brooksy

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:

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

**brooksy** · November 24th 2008, 04:43 AM

thanks.

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