What is the inverse of e^{sqrt(x+x^2)} ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

inverse of e^{sqrt(x+x^2)}

inverse

e^{x + x^{2}}

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

x^{2} - 1

(- 2, - 4), (1, - 7)

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

f (x) = - 2 x^{3} - 8 x^{2} + 10 x

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