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)/(1+x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

inverse

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

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

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}{1 + x})

f (x) = \frac{x ^{3} - 27}{x - 3}

f (x) = x + 6 + 3

f (x) = ln (\frac{x}{18})

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

f (x) = 5^{x + 1}

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)/(1+x))