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

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

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

inverse

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

x - ln (e^{x} - 1)

Solution steps

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

Replace

x

with

y

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

Solve for

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

x - ln (e^{x} - 1)

f (x) = \frac{3 x - 1}{2 x + 1}

f (x) = ln (x^{2} - 4) + π

\frac{3 x - 4}{2 - x}

\frac{5 - 3 x}{2 x - 3}

f (x) = 0.2 x + 5.3

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