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

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

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

inverse

e^{x^{2} - 2 x}

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

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

f (x) = \frac{9 x - 6}{6 x - 7}

f (x) = 4 x - 215

\frac{5 - 2 x}{4 x - 2}

\frac{3 - 2 x}{x - 5}

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

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