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Question: 1 20 points let f and g be bounded functions...

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1. (20 points) Let f and g be bounded functions from a nonempty set X into R. Let f(X) (a) Prove that if f(r) g(z) for all r in X, then inff(X) < înfg(X) and sup f(X) sup g(X). (b) Prove that if f) g(u) for all r and y in X, then sup f(X) S inf g(X). (c) Give an example showing that the hypothesis of part (a) does not imply the conclusion of g(x) xe part (b)

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