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))

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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)

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))