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Are these properties of real variable functions simply defined as they are, or is there another explanation?

$(f+g)(x) = f(x)+g(x)$

$(fg)(x) = f(x)g(x)$

$(af)(x) = af(x)$

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    $\begingroup$ Summation, multiplication, and scalar multiplication of functions are simply defined by the formulas you wrote down. So, yes, these are defined this way. $\endgroup$
    – David Gao
    Apr 3 at 1:11

1 Answer 1

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They are simply defined this way!

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