What is the inverse of f(x)=(1-e^{6x})/(1+e^{6x)} ?

The inverse of f(x)=(1-e^{6x})/(1+e^{6x)} is (ln((1-x)/(x+1)))/6

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inverse of f(x)=(1-e^{6x})/(1+e^{6x)}

inverse

f (x) = \frac{1 - e ^{6 x}}{1 + e ^{6 x}}

\frac{ln ( \frac{1 - x}{x + 1} )}{6}

Solution steps

y = \frac{1 - e ^{6 x}}{1 + e ^{6 x}}

Replace

x

with

y

x = \frac{1 - e ^{6 y}}{1 + e ^{6 y}}

Solve for

y, x = \frac{1 - e ^{6 y}}{1 + e ^{6 y}}

\frac{ln ( \frac{1 - x}{x + 1} )}{6}

What is the inverse of f(x)=(1-e^{6x})/(1+e^{6x)} ?
The inverse of f(x)=(1-e^{6x})/(1+e^{6x)} is (ln((1-x)/(x+1)))/6