What is the inverse of f(x)=16x-4x^2 ?

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

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inverse of f(x)=16x-4x^2

inverse

f (x) = 16 x - 4 x^{2}

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

Solution steps

y = 16 x - 4 x^{2}

Replace

x

with

y

x = 16 y - 4 y^{2}

Solve for

y, x = 16 y - 4 y^{2}

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

f (x) = 9 + 4 x - 4

f (x) = - \frac{4}{x - 1} - 2

\frac{8 x + 9}{3 x - 8}

f (x) = \frac{1}{2 x + 7}

\frac{3}{5} x - 15

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