What is the inverse of f(x)=6x-x^2 ?

The inverse of f(x)=6x-x^2 is 3-sqrt(-x+9),sqrt(-x+9)+3

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inverse of f(x)=6x-x^2

inverse

f (x) = 6 x - x^{2}

3 - - x + 9, - x + 9 + 3

Solution steps

y = 6 x - x^{2}

Replace

x

with

y

x = 6 y - y^{2}

Solve for

y, x = 6 y - y^{2}

3 - - x + 9, - x + 9 + 3

- x^{3} + 8 x^{2} - 15 x

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

(- 2, - 6), (4, 6)

y = 8 x - 7

\frac{- 6 x + 23}{7 x - 16}

What is the inverse of f(x)=6x-x^2 ?
The inverse of f(x)=6x-x^2 is 3-sqrt(-x+9),sqrt(-x+9)+3