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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)=(2(-x)^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

    CompuChip

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    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

    ehild

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    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.

    ehild
     
  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

    HallsofIvy

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    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.
     
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