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) = \frac{x ^{2} - 1}{x ^{2} + 1}

3 x - 2

4 x + 2 y = - 20

y = 2 sin (x)

(- 10, - 9), (0, 1)

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))