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:
- $f$ is injective but not surjective
- $f$ is surjective but not injective
- $f$ is neither injective nor surjective
- $f$ is bijective