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Homework Help: Odd vs even

  1. Oct 6, 2004 #1
    the rule for an odd function is: -f(x)=f(x) correct?

    however, x^3 is odd? Why is that? -(x^3) != (x^3)


    Also, how would someone tell if a function is odd or even if it was an equation like: (x^7)(x^6)/(x^4) or something of that nature?
     
  2. jcsd
  3. Oct 6, 2004 #2

    Gokul43201

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    You've got the definition wrong. You're essentially stating that -something = something. This is true only if something = 0.

    Correct definition : If f(-x) = -f(x), then f is odd.
     
  4. Oct 6, 2004 #3
    ahhh okay! That makes sense! What about telling if a function is odd or even if it was an equation like: (x^7)(x^6)/(x^4) or something similar to that?
     
  5. Oct 6, 2004 #4

    Gokul43201

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    What you've written can be simplified to x^9. (since [itex]x^ax^b = x^{a+b}[/itex])

    Odd powers of a variable are odd functions. And even powers are even functions.
     
  6. Oct 6, 2004 #5

    arildno

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    Plug in -x at the x place. If what comes out of f(-x) is EXACTLY -f(x), then your function is odd.
     
  7. Oct 6, 2004 #6
    what if a function was...[(x^7)+(x^6)]/(x^4)
     
  8. Oct 6, 2004 #7

    Gokul43201

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    [itex]f(x) = x^3 + x^2 [/itex] is neither odd nor even, (this is what your example simplifies to). See why this is true, by applying the definition.
     
  9. Oct 6, 2004 #8
    Because the exponet is an odd and even number? So it's neither. Does the sign make any difference? Positive or negative? what if a function was...[(x^7)+(x^6)]/[(x^4)-(x^3)]
     
  10. Oct 6, 2004 #9

    Gokul43201

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    Read post #5.
     
  11. Oct 6, 2004 #10
    I get the point :smile: thanks
     
  12. Dec 8, 2004 #11
    What if the function is defined differently at different intervals? How would I then go about finding out whether it's odd or even?
     
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