Let f, g : [0, 1] → [0, 1] be function. Let R(f) and R(g) be the ranges of f and g, respectively. Which of the following statements is/are true?
1
If f(x) ≤ g(x) for all x ∈ [0, 1], then sup R(f) ≤ inf R(g)
2
If f(x) ≤ g(x) for some x ∈ [0, 1], then inf R(f) ≤ sup R(g)
3
If f(x)g(y)for some x, y ∈ [0, 1], then inf R(f) ≤ sup R(g)
4
If f(x) ≤ g(y) for all x, y ∈ [0, 1], then sup R(f) ≤ inf R(g)