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

The inverse of f(x)=4x(4-x) is -(-4+sqrt(-x+16))/2 ,(sqrt(-x+16)+4)/2

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

inverse

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

- \frac{- 4 + - x + 16}{2}, \frac{- x + 16 + 4}{2}

Solution steps

y = 4 x (4 - x)

Replace

x

with

y

x = 4 y (4 - y)

Solve for

y, x = 4 y (4 - y)

- \frac{- 4 + - x + 16}{2}, \frac{- x + 16 + 4}{2}

f (x) = 3 (x - 2)^{2} - 4

f (x) = \frac{2 x - 5}{x + 1}

f (x) = \frac{6 - x}{2}

f (x) = 3 x - 2 + 4

f (x) = \frac{3 x + 1}{x + 3}

What is the inverse of f(x)=4x(4-x) ?
The inverse of f(x)=4x(4-x) is -(-4+sqrt(-x+16))/2 ,(sqrt(-x+16)+4)/2