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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

f (x) = 2 - 3

f (x) = 2^{3} - 1

x^{4} - 8 x^{2} + 17

f (2) = 3 x - 7

f (x) = 5

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