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

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

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

inverse

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

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

Solution steps

y = x - x^{2}

Replace

x

with

y

x = y - y^{2}

Solve for

y, x = y - y^{2}

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

y = x + 5 - 3

f (x) = - 8 x^{2} + 7

f (x) = 8 + 2 x - 2

27 cos^{2} (3 x)

f (x) = 6 - 2 x

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