Let $$A = \{x \in R : x$$ is not a positive integer$$\}$$. Define a function $$f: A \to R$$ as $$f(x) = \frac{2x}{x-1}$$, then $$f$$ is:

A

Injective but not surjective

B

Not injective

C

Surjective but not injective

D

Neither injective nor surjective