Question: If the product function h(x) = (x) g(x) is continuous at x = 0, must (x) and g(x) be continuous at x = 0?

If the product function h(x) = ƒ(x) · g(x) is continuous at x = 0, must ƒ(x) and g(x) be continuous at x = 0? Give reasons for your answer.

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