What is the inverse of f(x)=2x(4-x) ?

The inverse of f(x)=2x(4-x) is -(-8+sqrt(64-8x))/4 ,-(-8-sqrt(64-8x))/4

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inverse of f(x)=2x(4-x)

inverse

f (x) = 2 x (4 - x)

- \frac{- 8 + 64 - 8 x}{4}, - \frac{- 8 - 64 - 8 x}{4}

Solution steps

y = 2 x (4 - x)

Replace

x

with

y

x = 2 y (4 - y)

Solve for

y, x = 2 y (4 - y)

- \frac{- 8 + 64 - 8 x}{4}, - \frac{- 8 - 64 - 8 x}{4}

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

f (x) = 9 x - 6

f (x) = 9 x^{3} + 4

f (x) = - \frac{5}{4} x - 6

What is the inverse of f(x)=2x(4-x) ?
The inverse of f(x)=2x(4-x) is -(-8+sqrt(64-8x))/4 ,-(-8-sqrt(64-8x))/4