What is the inverse of (3e^x+1)/(9e^x-1) ?

The inverse of (3e^x+1)/(9e^x-1) is ln((1+x)/(3(-1+3x)))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

inverse of (3e^x+1)/(9e^x-1)

inverse

\frac{3 e ^{x} + 1}{9 e ^{x} - 1}

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

Solution steps

y = \frac{3 e ^{x} + 1}{9 e ^{x} - 1}

Replace

x

with

y

x = \frac{3 e ^{y} + 1}{9 e ^{y} - 1}

Solve for

y, x = \frac{3 e ^{y} + 1}{9 e ^{y} - 1}

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

f (x) = \frac{50 x + 1000}{x}

f (x) = \frac{1 - 3 ^{2 x}}{9 ^{x} - 3}

- 2 x^{2} + 24 x

f (x) = \frac{5 - 2 x}{4 x - 1}

What is the inverse of (3e^x+1)/(9e^x-1) ?
The inverse of (3e^x+1)/(9e^x-1) is ln((1+x)/(3(-1+3x)))