Question: Exercise 3.4.5: Let A, B be intervals. Let f : A -> R and g: B - R be uniformly continuous functions such that f(x)

Exercise 3.4.5: Let A, B be intervals. Let f : A -> R and g: B - R be uniformly continuous functions such that f(x) = g(x) for x E AnB. Define the function h: AUB - R by h(x) := f(x) if x E A and h(x) := g(x) if XEB\\A. a) Prove that if AnB # 0, then h is uniformly continuous. b) Find an example where AnB = 0 and h is not even continuous

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