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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

inverse of f(x)=(ln(x)+3)/(1-2ln(x))

inverse

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

e^{- \frac{3 - x}{1 + 2 x}}

Solution steps

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

Replace

x

with

y

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

Solve for

y, x = \frac{ln ( y ) + 3}{1 - 2 ln ( y )}

e^{- \frac{3 - x}{1 + 2 x}}

f (x) = 5 ln (\frac{x + 2}{3})

f (x) = 2^{x + 3}

f (x) = \frac{2 x}{3 x + 8}

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

f (x) = 3 (x - 9)

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