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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

ln (x - 4)

7 x e^{x} csc (x)

\frac{4}{x ^{2}}

f (x) = \frac{1}{x - 8}

x^{3} - 9 x^{2} + 15 x + 3

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