Question

what's the inverse function of f(x)=x/(x-2)?

Answer 1

Sorry dont know

Answer 2

Let \(f(x) = y\)

Answer 3

\[y = \frac{x}{x-2}\]

Answer 4

Find \(x\) in terms of \(y\)..

Answer 5

\[y(x-2) = x \\ xy - 2y = x \\ xy - x = 2y \\ x(y-1) = 2y \\ x = \frac{2y}{y-1}\]

Answer 6

Now, just replace \(x\) with \(y\) and \(y\) with \(x\)..

Answer 7

\[y = \frac{2x}{x-1}\]

Answer 8

This is your inverse function..

Answer 9

thank you so much!