What is the inverse of sqrt((e^x-5)/(4-e^x)) ?

The inverse of sqrt((e^x-5)/(4-e^x)) is ln(-(-5-4x^2)/(x^2+1))

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inverse of sqrt((e^x-5)/(4-e^x))

inverse

\frac{e ^{x} - 5}{4 - e ^{x}}

ln (- \frac{- 5 - 4 x ^{2}}{x ^{2} + 1})

Solution steps

y = \frac{e ^{x} - 5}{4 - e ^{x}}

Replace

x

with

y

x = \frac{e ^{y} - 5}{4 - e ^{y}}

Solve for

y, x = \frac{e ^{y} - 5}{4 - e ^{y}}

ln (- \frac{- 5 - 4 x ^{2}}{x ^{2} + 1})

What is the inverse of sqrt((e^x-5)/(4-e^x)) ?
The inverse of sqrt((e^x-5)/(4-e^x)) is ln(-(-5-4x^2)/(x^2+1))