Determine whether f is even, odd, or neither?

  1. I've tried looking through my book to see how to do these, but I just can't find it. Any help would be appreciated:

    1) f(x) = 2x^5 - 3x^2 +2

    2) f(x) = x^3 - x^7

    3) f(x) = (1-x^2)/(1+x^2)

    4) f(x) = 1/(x+2)

    Thanks in advance!
     
  2. jcsd
  3. Dr Transport

    Dr Transport 1,507
    Science Advisor
    Gold Member

    the definition of an even and an odd function is as follows:

    [tex] f(-x) = f(x) [/tex] is and even function and

    [tex] f(-x) = -f(x) [/tex] is an odd function.
     
  4. Alright, I think I get it, thanks.
     
  5. HallsofIvy

    HallsofIvy 40,803
    Staff Emeritus
    Science Advisor

    It is also true (easy to prove) that a rational function (polynomial or quotient of polynomials) is even if and only if all exponents of x are even, odd if and only if all exponents of x are odd.

    Of course, functions don't always have "exponents"! sin(x) is an odd function and cos(x) is an even function.
     
  6. But the series expansions precisely consist of only odd-numbered and only even-numbered polynomial terms, respectively. It's quite elegant.
     
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