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Let $f(x) = \dfrac{2x}{x-1}, \: x \neq 1$. State which of the following statements is true.

- For all real $y$, there exists $x$ such that $f(x)=y$
- For all real $y \neq 1$, there exists $x$ such that $f(x)=y$
- For all real $y \neq 2$, there exists $x$ such that $f(x)=y$
- None of the above is true