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Atypical definition of decreasing function

  1. Mar 8, 2006 #1
    1 few days ago i saw a "strange" definition of a decreasing function in the web, but i cant 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:
    [tex]f(x)=\frac{1}{x}[/tex]
    does it look familiar?

    2 there is a function:
    [tex]f(x)=\frac{2x+cos {x}}{3+x^{2}}[/tex]
    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? ;/
     
  2. jcsd
  3. Mar 8, 2006 #2

    quasar987

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    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.
     
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