Atypical definition of decreasing function

[rahl__]

1 few days ago i saw a "strange" definition of a decreasing function in the web, but i can't find it now. there were three relationships, and when showing that one implies another, you could tell that the function is decreasing. one relationship looked like this:
f(x)=\frac{1}{x}
does it look familiar?

2 there is a function:
f(x)=\frac{2x+cos {x}}{3+x^{2}}
how can find if it is periodic[al?]? I've heard that the polynomial of an odd degree is not periodic[al], can I use this principle to define whether that function is periodic[al] or not? does this principle say[tell? sorry for this ungrammatical statement], that there are some polynomials of an even degree that are periodic[al]?

3 is it spelt periodic or periodical? ;/

 

[quasar987]

2 What you have here is not a polynomial. It's not even a quotient of polynomials. The general idea when trying to get determinethe period (if it exists) of a function is simply to write f(x) = f(x+L) and solve for L. If L is of the form kP (k integer), then P is your period.