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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

f (x) = - 16 x^{2}

f (x) = 6 x + 1

\frac{1}{2} x + \frac{3}{2}

f (x) = 3 x + 24

7 x^{2} + 3

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