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

The inverse of f(x)=5x-x^2 is -(-5+sqrt(25-4x))/2 ,-(-5-sqrt(25-4x))/2

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inverse of f(x)=5x-x^2

inverse

f (x) = 5 x - x^{2}

- \frac{- 5 + 25 - 4 x}{2}, - \frac{- 5 - 25 - 4 x}{2}

Solution steps

y = 5 x - x^{2}

Replace

x

with

y

x = 5 y - y^{2}

Solve for

y, x = 5 y - y^{2}

- \frac{- 5 + 25 - 4 x}{2}, - \frac{- 5 - 25 - 4 x}{2}

5^{x} - 4

f (x) = 1 0^{(x - 2)} - 5

f (x) = x^{3} - 9 x^{2} - 21 x + 2

- x + 9

4 x^{3} - 25 x - 4 x

What is the inverse of f(x)=5x-x^2 ?
The inverse of f(x)=5x-x^2 is -(-5+sqrt(25-4x))/2 ,-(-5-sqrt(25-4x))/2