Question: Could you help with this please? Q2 From Q1, we know that d.(f. 9) = sup(|f(x) -g(x)| : re /} defines a metric on C(I)

Could you help with this please?

Q2 From Q1, we know that d.(f. 9) = sup(|f(x) -g(x)| : re /} defines a metric on C(I) where I = [0, 1]. [12 marks] (a) Does this still define a metric if the interval / is changed to / = (0, 1)? Explain your answer. (b) Does this still define a metric if / = R? Explain your answer. (c) What if, instead of continuous functions on / = 0, 1), we considered the set of all bounded functions on /? Briefly explain your

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