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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

\frac{1 - 3 x}{x + 2}

f (x) = 6 + x

f (x) = \frac{- 25 - 2 x}{5}

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

y = \frac{4}{- x - 2} + 2

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