What is the inverse of f(x)=-5x^2+10x+20 ?

The inverse of f(x)=-5x^2+10x+20 is -(-10+sqrt(-20x+500))/(10),-(-10-sqrt(-20x+500))/(10)

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inverse of f(x)=-5x^2+10x+20

inverse

f (x) = - 5 x^{2} + 10 x + 20

- \frac{- 10 + - 20 x + 500}{10}, - \frac{- 10 - - 20 x + 500}{10}

Solution steps

y = - 5 x^{2} + 10 x + 20

Replace

x

with

y

x = - 5 y^{2} + 10 y + 20

Solve for

y, x = - 5 y^{2} + 10 y + 20

- \frac{- 10 + - 20 x + 500}{10}, - \frac{- 10 - - 20 x + 500}{10}

What is the inverse of f(x)=-5x^2+10x+20 ?
The inverse of f(x)=-5x^2+10x+20 is -(-10+sqrt(-20x+500))/(10),-(-10-sqrt(-20x+500))/(10)