What is the inverse of f(x)=1000x-2x^2 ?

The inverse of f(x)=1000x-2x^2 is -(-1000+sqrt(1000000-8x))/4 ,-(-1000-sqrt(1000000-8x))/4

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inverse of f(x)=1000x-2x^2

inverse

f (x) = 1000 x - 2 x^{2}

- \frac{- 1000 + 1000000 - 8 x}{4}, - \frac{- 1000 - 1000000 - 8 x}{4}

Solution steps

y = 1000 x - 2 x^{2}

Replace

x

with

y

x = 1000 y - 2 y^{2}

Solve for

y, x = 1000 y - 2 y^{2}

- \frac{- 1000 + 1000000 - 8 x}{4}, - \frac{- 1000 - 1000000 - 8 x}{4}

x^{2} - 6 x + 11

y = - λ ln (x)

y = \frac{1 - 3 ^{2 x}}{9 ^{x} - 3}

f (x) = \frac{3 x}{8 x - 5}

f (x) = \frac{( 9 - x ^{2} )}{4}

What is the inverse of f(x)=1000x-2x^2 ?
The inverse of f(x)=1000x-2x^2 is -(-1000+sqrt(1000000-8x))/4 ,-(-1000-sqrt(1000000-8x))/4