What is the inverse of f(x)=x(3-x) ?

The inverse of f(x)=x(3-x) is -(-3+sqrt(9-4x))/2 ,-(-3-sqrt(9-4x))/2

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inverse of f(x)=x(3-x)

inverse

f (x) = x (3 - x)

- \frac{- 3 + 9 - 4 x}{2}, - \frac{- 3 - 9 - 4 x}{2}

Solution steps

y = x (3 - x)

Replace

x

with

y

x = y (3 - y)

Solve for

y, x = y (3 - y)

- \frac{- 3 + 9 - 4 x}{2}, - \frac{- 3 - 9 - 4 x}{2}

f (x) = \frac{3 x + 6}{2}

f (x) = arcsin (- \frac{2}{2})

5 - x + 6

f (x) = x^{3} + 1

- 3 x - 5

What is the inverse of f(x)=x(3-x) ?
The inverse of f(x)=x(3-x) is -(-3+sqrt(9-4x))/2 ,-(-3-sqrt(9-4x))/2