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

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

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

inverse

f (x) = 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) = 3 - 4 - x

2 π r^{2} + 8 π r

f (x) = 2 π x^{2} + 12 π x

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

f (x) = - 2 (x - 3)^{2} - 6

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