Let the set X = (-1, 1)

Question

Define f: X--->R(set of real numbers) such that f(x) = x/(x-1)

Check if f is onto.

Let y = x/(x-1)
Then, x = y/(y-1)

Since y belongs to R, y=1 would result in an undefined value for x.

Hence, can we conclude f is not onto?