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

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

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inverse of f(x)=2x-x^2

inverse

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

1 - - x + 1, - x + 1 + 1

Solution steps

y = 2 x - x^{2}

Replace

x

with

y

x = 2 y - y^{2}

Solve for

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

1 - - x + 1, - x + 1 + 1

2 - x^{2}

f (x) = 3 x (2 - x)

f (x) = \frac{1}{x}

e^{2 t}

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