Every continuous smooth real function f(x) is either odd , even, or sum/difference of an even and odd (mixed like e.g., exponential) functions. Is this generally correct?
Can the even part of a mixed f(x) and odd part of another mixed g(x) be combined to make a new combo h(x)? If so how so and if not why not?
Do such hybrid h(x) satisfy mean value theorem? Will there be no problem with computing their curvatures and inflection points? I asked this as I somehow feel that a mixed Taylor series has some of its " chemistry" or nature altered.