What is the inverse of f(x)=12x-x^2 ?

The inverse of f(x)=12x-x^2 is 6-sqrt(-x+36),sqrt(-x+36)+6

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inverse of f(x)=12x-x^2

inverse

f (x) = 12 x - x^{2}

6 - - x + 36, - x + 36 + 6

Solution steps

y = 12 x - x^{2}

Replace

x

with

y

x = 12 y - y^{2}

Solve for

y, x = 12 y - y^{2}

6 - - x + 36, - x + 36 + 6

2 x - x^{2}

\frac{1}{3} x + 2

\frac{x + 1}{2}

f (x) = \frac{x}{x + 1} + 1

What is the inverse of f(x)=12x-x^2 ?
The inverse of f(x)=12x-x^2 is 6-sqrt(-x+36),sqrt(-x+36)+6