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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

inverse

f (x) = \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})

\frac{3 x - 2}{5 - 2 x}

f (x) = \frac{( 4 x - 5 )}{x - 4}

arcsin (0.3)

- x - 8

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