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Show that if f is continuous on the closed interval a b

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Reference no: EM13591216

(a) Show that if f is continuous on the closed interval [a, b], then there is a function g which is continuous on R, and which satisfies g(x) = f(x) for all x in [a, b].

(b) Give an example to show that the previous assertion is false if [a, b] is replaced by the open interval (a, b).

Reference no: EM13591216

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