Given real-valued functions f and g with the same domain D, the sum of f and g, denoted

Chapter 11, Problem 20

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Given real-valued functions f and g with the same domain D, the sum of f and g, denoted f + g, is defined as follows:

For all real numbers x, (f + g)(x) = f(x) + g(x).

Show that if f and g are both increasing on a set S, then f + g is also increasing on S.

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