What is the inverse of f(x)=(1+e^x)/(1-e^x) ?

The inverse of f(x)=(1+e^x)/(1-e^x) is ln(-(1-x)/(1+x))

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inverse of f(x)=(1+e^x)/(1-e^x)

inverse

f (x) = \frac{1 + e ^{x}}{1 - e ^{x}}

ln (- \frac{1 - x}{1 + x})

Solution steps

y = \frac{1 + e ^{x}}{1 - e ^{x}}

Replace

x

with

y

x = \frac{1 + e ^{y}}{1 - e ^{y}}

Solve for

y, x = \frac{1 + e ^{y}}{1 - e ^{y}}

ln (- \frac{1 - x}{1 + x})

What is the inverse of f(x)=(1+e^x)/(1-e^x) ?
The inverse of f(x)=(1+e^x)/(1-e^x) is ln(-(1-x)/(1+x))