Question: Find examples of two disjoint, non-empty sets A,B C R and a function f: AUB-R such that flA and flB are each uniformly continuous but

Find examples of two disjoint, non-empty sets A,B C R and a function f: AUB-R such that flA and flB are each uniformly continuous but f is not uniformly continuous. (NOTE: f|A and f|B represent f restricted to A and f restricted to B, respectively.)

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