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})

g (x) = x - 5 + 2

f (x) = (1 + 7 x)^{8}

f (x) = \frac{- 3 - 4 x}{2 + 2 x}

f (x) = \frac{1}{2 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))