JEE Math Practice Question

Let f : A $$ \to $$ B be a function defined as f(x) = $${{x - 1} \over {x - 2}},$$ Where A = R $$-$$ {2} and B = R $$-$$ {1}. Then f is :

1. A.invertible and $${f^{ - 1}}(y) = $$ $${{3y - 1} \over {y - 1}}$$
2. B.invertible and $${f^{ - 1}}\left( y \right) = {{2y - 1} \over {y - 1}}$$
3. C.invertible and $${f^{ - 1}}\left( y \right) = {{2y + 1} \over {y - 1}}$$
4. D.not invertible