Let f;x =(x+1)/(x-2) be a function defined on the set of real number excluding 2. Find f^1?

To find the inverse of the function f(x) = (x+1)/(x-2), we first need to switch the roles of x and y and then solve for y.

So, let y = (x+1)/(x-2)

Switching x and y, we get x = (y+1)/(y-2)

Now, solve for y:

x(y-2) = y + 1
xy - 2x = y + 1
xy - y = 2x + 1
y(x-1) = 2x + 1
y = (2x + 1)/(x-1)

Therefore, the inverse function of f(x) is f^(-1)(x) = (2x + 1)/(x-1)