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

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

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inverse of (1-e^{2x})/(2+e^{2x)}

inverse

\frac{1 - e ^{2 x}}{2 + e ^{2 x}}

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

Solution steps

y = \frac{1 - e ^{2 x}}{2 + e ^{2 x}}

Replace

x

with

y

x = \frac{1 - e ^{2 y}}{2 + e ^{2 y}}

Solve for

y, x = \frac{1 - e ^{2 y}}{2 + e ^{2 y}}

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

f (x) = 8 x - x^{2}

f (x) = ln (y)

f (x) = x + 1 - 6

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

ln (6 - 2 X)

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