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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

f (x) = 4 x

f (x) = - 4 sin (2 x - 7) + 3

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

f (x) = 9 - x^{2}

\frac{- 3 x ( x - 2 )}{( x - 2 ) ( x + 2 )}

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