Question: Suppose that f'(x) > 0 and g'(x) > 0 for all x. What simple additional conditions (if any) are needed to guarantee that: (a) f(x)

Suppose that f'(x) > 0 and g'(x) > 0 for all x. What simple additional conditions (if any) are needed to guarantee that:
(a) f(x) + g(x) is increasing for all x;
(b) f(x) ∙ g(x) is increasing for all x;
(c) f(g(x)) is increasing for all x?

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