Hi everyone....solve this !!!find the range and domain of the function f(x) = (2x+1)/(x-1)and also find its inverse.

This function is not defined for x = 1. So, domain of the function is
R -{1}.

Now, for finding the range

Let,(2x+3)/(x-1) = y

        => 2x + 3 = yx - y

        => yx - 2x = y + 3

        => (y - 2)x = y + 3

        => x =(y+3)/(t-2)

So, y cannot assume value 2

Range of f(x) is R - {2}.

Inverse is y =(x+3/x-2) .