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Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be a continuous function such that :

                     $\left | f\left ( x \right ) -f\left ( y \right )\right |\geq log\left ( 1+\left | x-y \right | \right ),$ for all $x,y \in \mathbb{R}$.

Then:

  1. $f$ is injective but not surjective
  2. $f$  is surjective but not injective
  3. $f$ is neither injective nor surjective
  4. $f$ is bijective
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