Given real-valued functions f and g with the same domain D, the sum of f and g, denoted
, is defined as follows:
For each real number .
Show that if f and g are both increasing on a set S. then is also increasing on S.
If and are both increasing on a set , then is also increasing on .
Suppose is increasing.
Given real valued functions with the same domain , the sum of , denoted , is defined as follows.
For all real numbers .
It is given that are real valued functions defined on the same domain . Let where a non-empty subset of is .
Is an increasing function on a set, so for .
Is an increasing function on a set, so for
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