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Let $f : \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function such that $|f(x)−f(y)| \geq \frac{1}{2}|x−y|$, for all $x, y \in \mathbb{R}$ . Then 

  1. $f$ is both one-to-one and onto 
  2. $f$ is one-to-one but may not be onto 
  3. $f$ is onto but may not be one-to-one 
  4. $f$ is neither one-to-one nor onto
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