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

The inverse of (e^x-e^{-x})/(e^x+e^{-x)} is 1/2 ln((-1-x)/(x-1)),ln(-sqrt((-1-x)/(x-1)))

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

inverse

\frac{e ^{x} - e ^{- x}}{e ^{x} + e ^{- x}}

\frac{1}{2} ln (\frac{- 1 - x}{x - 1}), ln (- \frac{- 1 - x}{x - 1})

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{1}{2} ln (\frac{- 1 - x}{x - 1}), ln (- \frac{- 1 - x}{x - 1})

f (x) = \frac{( x - 1 )}{3}

\frac{x}{4}

f (x) = - 10 x + 8

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

f (x) = - 2 x + 1 - 3

What is the inverse of (e^x-e^{-x})/(e^x+e^{-x)} ?
The inverse of (e^x-e^{-x})/(e^x+e^{-x)} is 1/2 ln((-1-x)/(x-1)),ln(-sqrt((-1-x)/(x-1)))