What is the inverse of f(x)=ln((1+x)/(1-x)) ?

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

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inverse of f(x)=ln((1+x)/(1-x))

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

y, x = ln (\frac{1 + y}{1 - y})

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

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