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

The inverse of f(x)=(x^2)/(x-6) is (x+sqrt(x^2-24x))/2 ,(x-sqrt(x^2-24x))/2

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

inverse

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

\frac{x + x ^{2} - 24 x}{2}, \frac{x - x ^{2} - 24 x}{2}

Solution steps

y = \frac{x ^{2}}{x - 6}

Replace

x

with

y

x = \frac{y ^{2}}{y - 6}

Solve for

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

\frac{x + x ^{2} - 24 x}{2}, \frac{x - x ^{2} - 24 x}{2}

(2, - 5), (6, - 2)

(4, - 5), (0, 0)

- \frac{1}{9} x^{3} - 3

f (x) = (x - 4)^{2} + 1

f (x) = 10 x - 9

What is the inverse of f(x)=(x^2)/(x-6) ?
The inverse of f(x)=(x^2)/(x-6) is (x+sqrt(x^2-24x))/2 ,(x-sqrt(x^2-24x))/2