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See: Types of Functions

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Is there any other type of function left outside this classification?

user366312
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  • where do you classify $x^x$? – Tito Eliatron Dec 27 '18 at 18:40
  • $F(x)=\int_0^x e^{-t^2}dt$ seems to be outside – Tito Eliatron Dec 27 '18 at 18:41
  • @TitoEliatron, regarding your 1st comment: I don't know. regarding your second comment: that is an exponential function. – user366312 Dec 27 '18 at 18:42
  • See this wiki page, I think you have a fair few more types to add :P https://en.m.wikipedia.org/wiki/Function_space?wprov=sfla1 – Eddy Dec 27 '18 at 18:43
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    @stackoverflow.com The first comment: $x^x=e^{x\log x}$, so it may be a mixed exp-log function.

    For the second, It is the Primitive of an exponetial function, but as far as I know, it cannot be expressed by elementary functions. So I think it is NOT exponential

     – Tito Eliatron Dec 27 '18 at 18:44
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    Also https://en.m.wikipedia.org/wiki/List_of_mathematical_functions?wprov=sfla1 – Eddy Dec 27 '18 at 18:46
  • But if you limit your question to a specific course/exam (not relevant to this site) then that classification might be sufficient, even though it is able to classify only an incredibly tiny portion of all the functions. – Eddy Dec 27 '18 at 18:51
  • Hyperbolic functions $(\sinh, \cosh, \tanh)$ integer parts $[x]$ – Jonathan Bow Dec 27 '18 at 18:45
  • Hyperbolic functions are linear combinations of exponentials. Integer part is a Piecwise affine function. – Tito Eliatron Dec 27 '18 at 18:46
  • See Expanded concept of elementary function? – Dave L. Renfro Dec 27 '18 at 20:23
  • And an incredibly number of special functions. Among them standard special functions which list is never definitive. https://fr.scribd.com/doc/14623310/Safari-on-the-country-of-the-Special-Functions-Safari-au-pays-des-fonctions-speciales – JJacquelin Dec 28 '18 at 05:11
  • Also try classifying https://en.wikipedia.org/wiki/Weierstrass_function and https://en.wikipedia.org/wiki/Thomae's_function :) –  Dec 28 '18 at 16:50

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Continuous, discontinuous, differentiable, piecewise continuous, open, closed, compact supported, bounded, with bounded variation and many more besides all functions that have a domain or codomain other than the reals.

William Elliot
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