What is the inverse of f(x)=(2e^x-4)/(12e^x+11) ?

The inverse of f(x)=(2e^x-4)/(12e^x+11) is ln((-4-11x)/(2(-1+6x)))

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inverse of f(x)=(2e^x-4)/(12e^x+11)

inverse

f (x) = \frac{2 e ^{x} - 4}{12 e ^{x} + 11}

ln (\frac{- 4 - 11 x}{2 ( - 1 + 6 x )})

Solution steps

y = \frac{2 e ^{x} - 4}{12 e ^{x} + 11}

Replace

x

with

y

x = \frac{2 e ^{y} - 4}{12 e ^{y} + 11}

Solve for

y, x = \frac{2 e ^{y} - 4}{12 e ^{y} + 11}

ln (\frac{- 4 - 11 x}{2 ( - 1 + 6 x )})

What is the inverse of f(x)=(2e^x-4)/(12e^x+11) ?
The inverse of f(x)=(2e^x-4)/(12e^x+11) is ln((-4-11x)/(2(-1+6x)))