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inverse function

find the inverse of Ln(2x+1)

$y = ln(2x+1) \\ e^y = e^{ln(2x+1)} \\ e^y = 2x+1 \\ e^y - 1 = 2x \\ \frac{e^y - 1}{2} = x \\ f^{-1} = \frac{e^x - 1}{2}$

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