Question: Let f(x) and g(x) be continuous functions on [a, b]. Define f g(x) = min{f(x), g(x)} and f g(x) = max{f(x), g(x)}. Prove that f

Let f(x) and g(x) be continuous functions on [a, b]. Define f g(x) = min{f(x), g(x)} and f g(x) = max{f(x), g(x)}. Prove that f g and f g are continuous.

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