Let K ⊆ R be non-empty and f : K → K be continuous such that |x - y| ≤ f(x) - f(y)| ∀x, y ∈ K.
Which of the following statements are true?
1
f need not be surjective
2
f must be surjective if K = [0, 1]
3
f is injective and f-1 : f(K) → K is continuous
4
f is injective, but f-1 : f(K) → K need not be continuous