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

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

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

inverse

f (x) = x (2 - x)

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

Solution steps

y = x (2 - x)

Replace

x

with

y

x = y (2 - y)

Solve for

y, x = y (2 - y)

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

3 x - x^{2}

\frac{1}{4 x - 8}

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

f (x) = - x^{2} - x - 1

\frac{1}{4} x - \frac{1}{2}

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