1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Symmetry question

  1. Nov 2, 2011 #1
    1. The problem statement, all variables and given/known data
    is the function f(x) = (2x^2-x)/(x^2+x) even, odd, or neither?

    2. Relevant equations

    f(-x)=f(x) = even
    f(-x)=-f(x) = odd
    f(-x)≠f(x)≠ -f(x)

    3. The attempt at a solution
    f(x) = (2x^2-x)/(x^2+x)
    f(-x) = (2x^2+x)/(x^2-x)

    i think thats the right way to do it, but i don't know if it's even or odd.
  2. jcsd
  3. Nov 2, 2011 #2


    User Avatar
    Science Advisor
    Homework Helper

    That is the right way to do it.
    So you have found the explicit form of f(-x).
    Now is that equal to f(x), to -f(x), or neither?
  4. Nov 2, 2011 #3


    User Avatar
    Homework Helper

    Just try to substitute some value for x, say x=2 and x=-2. If f(2) is not equal either to f(-2) or -f(-2) than the function is neither odd nor even.

  5. Nov 2, 2011 #4
    judging that the signage is switched from the original function to the f(-x) and the square terms stayed the same, then the function is even?
  6. Nov 2, 2011 #5
    never saw it that way. thanks :)
  7. Nov 2, 2011 #6


    User Avatar
    Science Advisor

    While you can use that "counter-example" method to prove that a function is neither even nor odd (and most functions are), you cannot use it to prove a function is either even or odd. The fact that f(2)= f(-2) does NOT prove it happens for all x.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook