What is the inverse of f(x)=((e^x-3))/(2e^x+1) ?

The inverse of f(x)=((e^x-3))/(2e^x+1) is ln((-3-x)/(2x-1))

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inverse of f(x)=((e^x-3))/(2e^x+1)

inverse

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

ln (\frac{- 3 - x}{2 x - 1})

Solution steps

y = \frac{e ^{x} - 3}{2 e ^{x} + 1}

Replace

x

with

y

x = \frac{e ^{y} - 3}{2 e ^{y} + 1}

Solve for

y, x = \frac{e ^{y} - 3}{2 e ^{y} + 1}

ln (\frac{- 3 - x}{2 x - 1})

What is the inverse of f(x)=((e^x-3))/(2e^x+1) ?
The inverse of f(x)=((e^x-3))/(2e^x+1) is ln((-3-x)/(2x-1))