Constant functions

[Hom]

If f(g(x)) is a constant, is it necessary that either f or g is a constant function?

[yoyobarn]

I think it is not necessarily so.

Example: $$f(x)=e^{ix}$$
$$g(x)=2x\pi$$, if x is an integer, and 0 otherwise.

Then, $$f(g(x))=1$$ but neither f nor g are constant functions.

[Hom]

I think it is not necessarily so.

Example: $$f(x)=e^{ix}$$
$$g(x)=2x\pi$$, if x is an integer, and 0 otherwise.

Then, $$f(g(x))=1$$ but neither f nor g are constant functions.

Thank you yoyobarn. You're right. You inspired me to think of another case in R.
f(x) = sinx
g(x)= [x]*pi
f(g(x))=0

[owlpride]

Or g = f^{-1}.

[blitzer6266]

The identity? (gotta be honest, that was the first thing that came to my mind too.. not right though)

[owlpride]

Ooops. Lol!

That's what happens when you use 1_X to denote the identity function on X...