List of top Mathematics Questions on types of functions asked in KCET

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

Which of the following functions is not invertible?