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

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

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

inverse

f (x) = \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}

f (x) = x^{3} - 6 x^{2} + 1

(8.3) (4.7)

\frac{x}{x + 9}

f (x) = 5 - x

y = x^{5} - 5 x^{2} - 20 x - 2

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