Let f : [0, ∞) → ℝ be the periodic function of period 1 given by
f(x) = 1 - |2x - 1| for x ∈ [0, 1].
Further, define g : [0, ∞) → ℝ by g(x) = f(x2). Which of the following statements are true?
1
f is continuous on [0, ∞).
2
f is uniformly continuous on [0, ∞).
3
g is continuous on [0, ∞).
4
g is uniformly continuous on [0, ∞).