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Let $f:\mathbb{R}^{2}\rightarrow \mathbb{R}$ be a continuous map such that $f(x) = 0$ for only finitely many values of $x$. Which of the following is true?

  1. Either $f(x)\leq 0$ for all $x$, or, $f(x) \geq 0$ for all $x$ 
  2. The map $f$ is onto 
  3. The map $f$ is one-to-one 
  4. None of the above
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