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Math Help - can a function be both even and odd?

  1. #1
    Senior Member furor celtica's Avatar
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    Question can a function be both even and odd?

    can a function be both even and odd?
    Last edited by CaptainBlack; August 7th 2009 at 01:35 AM. Reason: Because I can
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  2. #2
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    I believe f(x) = 0 is the only polynomial function that is both even and odd. I don't know about the other functions (exponential, logarithmic, logistic, trigonometric,...).


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  3. #3
    Senior Member furor celtica's Avatar
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    well that clears that up. and for logarithmic, exponential, trigo?
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  4. #4
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    even ... f(-x) = f(x)

    odd ... f(-x) = -f(x)

    if even and odd, then f(x) = -f(x) ... what's that tell you?
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  5. #5
    Senior Member furor celtica's Avatar
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    do i take that as an absolute and true-in-all-cases 'no'? let's not be enigmatic please
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  6. #6
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    Quote Originally Posted by furor celtica View Post
    do i take that as an absolute and true-in-all-cases 'no'? let's not be enigmatic please
    it's your exercise ... put some thought into it.

    what function(s) is/are equal to its opposite?
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  7. #7
    Senior Member furor celtica's Avatar
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    even functions...
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  8. #8
    Member eXist's Avatar
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    Quote Originally Posted by furor celtica View Post
    even functions...
    I believe he's looking for some kind of trig function (Hopefully what I'm thinking of isn't wrong either) ^^
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  9. #9
    Grand Panjandrum
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    Quote Originally Posted by furor celtica View Post
    do i take that as an absolute and true-in-all-cases 'no'? let's not be enigmatic please
    Forget (for the moment) that we are talking about functions and just consider the value y of f(x) at the point x.

    As f is both odd and even y=f(x)=f(-x) and odd y=f(x)=-f(-x) and so:

    y=-y.

    Now what number/s (real or complex) is equal to minus times itself?

    But this is true for every value taken by f.

    CB
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