What is the inverse of f(x)=4x(6-x) ?

The inverse of f(x)=4x(6-x) is -(-6+sqrt(-x+36))/2 ,(sqrt(-x+36)+6)/2

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inverse of f(x)=4x(6-x)

inverse

f (x) = 4 x (6 - x)

- \frac{- 6 + - x + 36}{2}, \frac{- x + 36 + 6}{2}

Solution steps

y = 4 x (6 - x)

Replace

x

with

y

x = 4 y (6 - y)

Solve for

y, x = 4 y (6 - y)

- \frac{- 6 + - x + 36}{2}, \frac{- x + 36 + 6}{2}

f (x) = \frac{2 x + 4}{3}

f (x) = 9 (x + 3)^{\frac{1}{3}}

f (x) = 3 - x + 1

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

f (x) = \frac{5 + 3 x}{x - 1}

What is the inverse of f(x)=4x(6-x) ?
The inverse of f(x)=4x(6-x) is -(-6+sqrt(-x+36))/2 ,(sqrt(-x+36)+6)/2