Let $A = \{x \in R : x$ is not a positive integer$\}$. Define a function $f: A \rightarrow R$ as $f(x) = \frac{2x}{x-1}$, then $f$ is:\\
(1) Injective but not surjective\\
(2) Not injective\\
(3) Surjective but not injective\\
(4) Neither injective nor surjective