What is the inverse of f(x)=sqrt((e^x-6)/(3-e^x)) ?

The inverse of f(x)=sqrt((e^x-6)/(3-e^x)) is ln(-(-6-3x^2)/(x^2+1))

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inverse of f(x)=sqrt((e^x-6)/(3-e^x))

inverse

f (x) = \frac{e ^{x} - 6}{3 - e ^{x}}

ln (- \frac{- 6 - 3 x ^{2}}{x ^{2} + 1})

Solution steps

y = \frac{e ^{x} - 6}{3 - e ^{x}}

Replace

x

with

y

x = \frac{e ^{y} - 6}{3 - e ^{y}}

Solve for

y, x = \frac{e ^{y} - 6}{3 - e ^{y}}

ln (- \frac{- 6 - 3 x ^{2}}{x ^{2} + 1})

What is the inverse of f(x)=sqrt((e^x-6)/(3-e^x)) ?
The inverse of f(x)=sqrt((e^x-6)/(3-e^x)) is ln(-(-6-3x^2)/(x^2+1))