I have a couple of questions here..
I want to know if there is any standard algorithm that is followed to calculate the period of a given function..how do we arrive at the answer? For example: Compute the period of $$f(x)=\arctan(\tan(x))$$ I know that the answer is $\pi$ which I got after plotting $f(x)$..But is there a more formal way of arriving at this result..and any algorithm to do the same for other functions..In this case..the function is not reducible to any other form where we can use the fact that if $f(x)$ has T as its period..then $f(ax+b)$ has T/a as its period..
In the same way, how do we prove that certain functions are not periodic..(looking for an algorithm specifically..). For example prove that $$g(x)=x+\sin(x)$$ is not periodic..
Lastly, can we be sure that if $f(x)$ is periodic..then $g\circ f(x)$ is always periodic..if yes, then does it have the same period of $f(x)$..(Here $g$ is not necessarily periodic..). I'm looking for proofs of such statements here.
Thanks a lot for any answers!!
PS:I'm still in high school..so I dont understand any advanced topics in real analysis..