Constant functions
Constant functions
If f(g(x)) is a constant, is it necessary that either f or g is a constant function?
Re: Constant functions
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.
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.
Re: Constant functions
Thank you yoyobarn. You're right. You inspired me to think of another case in R.yoyobarn wrote: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.
f(x) = sinx
g(x)= [x]*pi
f(g(x))=0

 Posts: 61
 Joined: Sun Apr 04, 2010 1:08 pm
Re: Constant functions
The identity? (gotta be honest, that was the first thing that came to my mind too.. not right though)
Re: Constant functions
Ooops. Lol!
That's what happens when you use 1_X to denote the identity function on X...
That's what happens when you use 1_X to denote the identity function on X...