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

The inverse of f(x)=e^{2x}+e^x+1 is ln((-1+sqrt(4x-3))/2),ln((-1-sqrt(4x-3))/2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

inverse of f(x)=e^{2x}+e^x+1

inverse

f (x) = e^{2 x} + e^{x} + 1

ln (\frac{- 1 + 4 x - 3}{2}), ln (\frac{- 1 - 4 x - 3}{2})

Solution steps

y = e^{2 x} + e^{x} + 1

Replace

x

with

y

x = e^{2 y} + e^{y} + 1

Solve for

y, x = e^{2 y} + e^{y} + 1

ln (\frac{- 1 + 4 x - 3}{2}), ln (\frac{- 1 - 4 x - 3}{2})

f (x) = \frac{7 + 3 x}{2 x + 3}

lo g_{3} (27 x)

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

f (x) = 3 + 3 x - 8

g (x) = \frac{1 - x}{5}, x \leq 3

What is the inverse of f(x)=e^{2x}+e^x+1 ?
The inverse of f(x)=e^{2x}+e^x+1 is ln((-1+sqrt(4x-3))/2),ln((-1-sqrt(4x-3))/2)