JEE Math Practice Question

Let f : R $$\to$$ R be defined as f (x) = x $$-$$ 1 and g : R $$-$$ {1, $$-$$1} $$\to$$ R be defined as $$g(x) = {{{x^2}} \over {{x^2} - 1}}$$. Then the function fog is :

1. A.one-one but not onto
2. B.onto but not one-one
3. C.both one-one and onto
4. D.neither one-one nor onto