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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

f (x) = \frac{x}{5} - 9

3 x^{2} + 12 x - 7

y = \frac{x + 28}{x - 7}

1 + + (- 1)

y = \frac{5}{x ^{2} + 1}

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