What is the inverse of f(x)=x(x-1) ?

The inverse of f(x)=x(x-1) is (1+sqrt(1+4x))/2 ,(1-sqrt(1+4x))/2

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inverse of f(x)=x(x-1)

inverse

f (x) = x (x - 1)

\frac{1 + 1 + 4 x}{2}, \frac{1 - 1 + 4 x}{2}

Solution steps

y = x (x - 1)

Replace

x

with

y

x = y (y - 1)

Solve for

y, x = y (y - 1)

\frac{1 + 1 + 4 x}{2}, \frac{1 - 1 + 4 x}{2}

f (x) = x^{2} + 4 x - 24

f (x) = \frac{2}{3} x

3 x - 2 y = 6

3 x = - y - 5

f (x) = - 1 - x

What is the inverse of f(x)=x(x-1) ?
The inverse of f(x)=x(x-1) is (1+sqrt(1+4x))/2 ,(1-sqrt(1+4x))/2