What is the inverse of f(x)=x(1-x) ?

The inverse of f(x)=x(1-x) is -(-1+sqrt(1-4x))/2 ,-(-1-sqrt(1-4x))/2

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inverse of f(x)=x(1-x)

inverse

f (x) = x (1 - x)

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

Solution steps

y = x (1 - x)

Replace

x

with

y

x = y (1 - y)

Solve for

y, x = y (1 - y)

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

What is the inverse of f(x)=x(1-x) ?
The inverse of f(x)=x(1-x) is -(-1+sqrt(1-4x))/2 ,-(-1-sqrt(1-4x))/2