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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

inverse of f(x)=sqrt(e^{x^2-2x)}

inverse

f (x) = e^{x^{2} - 2 x}

1 + 1 + 2 ln (x), 1 - 1 + 2 ln (x)

Solution steps

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

Replace

x

with

y

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

Solve for

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

1 + 1 + 2 ln (x), 1 - 1 + 2 ln (x)

f (x) = 3 - 0.5 2 x + 4

f (x) = (\frac{3}{4}) (10 x - 2)

f (x) = 15 x^{2} + 8 x + 4

\frac{3 x ^{2} - 18 x + 24}{x ^{2} - 4 x}

f (x) = \frac{x ^{2} - 4}{x ^{2} + 9}

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