Teaching CSIR NET Mock Test Series Mathematical Science Analysis Point Set Topology

Let f : ℝ → ℝ be a continuous function such that |f(x) - f(y)| ≥ log(1 + |x - y|) for all x, y ∈ ℝ. Which of the following statements are true? 

1
f is necessarily one-one.
2
f need not be one-one.
3
f is necessarily onto.
4
f need not be onto.
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