Q2 From Q1, we know that du(f.g) = sup{f(r) - g(x): I} defines a metric on C(I) where I = [0, 1]. [12 marks] (a) Does this still define a metric if the interval I is changed to 7 = (0, 1)? Explain your answer. (b) Does this still define a metric if I = R? Explain your answer. (e) What if, instead of continuous functions on I = [0, 1], we considered the set of all bounded functions on I? Briefly explain your answer.