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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

\frac{9}{x ^{2} - 1}

(- 7.4) (1.8)

f (x) = 2 y - 3 x = - 8

x^{2} - x - 3

f (x) = - x^{2} + 6 x - 9

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