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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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