What is the inverse of f(x)=2x-0.5x^2 ?

The inverse of f(x)=2x-0.5x^2 is -(-20+sqrt(400-200x))/(10),-(-20-sqrt(400-200x))/(10)

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inverse of f(x)=2x-0.5x^2

inverse

f (x) = 2 x - 0.5 x^{2}

- \frac{- 20 + 400 - 200 x}{10}, - \frac{- 20 - 400 - 200 x}{10}

Solution steps

y = 2 x - 0.5 x^{2}

Replace

x

with

y

x = 2 y - 0.5 y^{2}

Solve for

y, x = 2 y - 0.5 y^{2}

- \frac{- 20 + 400 - 200 x}{10}, - \frac{- 20 - 400 - 200 x}{10}

f (x) = \frac{2 x + 4}{4 x + 5}

f (x) = 3 x - 1

sin (9 x)

y = - x + 11

(- 2.8) (2.2)

What is the inverse of f(x)=2x-0.5x^2 ?
The inverse of f(x)=2x-0.5x^2 is -(-20+sqrt(400-200x))/(10),-(-20-sqrt(400-200x))/(10)