Find a formula for the inverse of the function f(x)=(1+e^x)/(1-e^x)

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10-06-2018
Mathematics

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Find a formula for the inverse of the function f(x)=(1+e^x)/(1-e^x)

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harpazo harpazo · Answer 1 · 2018-06-10T19:31:30+02:00

harpazo harpazo

10-06-2018

Let y = f(x)

y = (1 + e^x)/(1 - e^x)

Exchange places with x and y.

x = (1 + e^y)/(1 - e^y)

Now solve for y.

y = log[(x + 1)/(x - 1)]

Replace y with the inverse notation.

f^(-1) x = log[(x + 1)/(x - 1)]

Done!

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