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Math Help - even and odd functions

  1. #1
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    even and odd functions

    Is there a function such that it is both even and odd?

    Is it f(x)=0? any others?
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  2. #2
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    A function is odd if \forall x, \ f(-x) = -f(x)

    A function is even if \forall x, \ f(-x) = f(x)

    Assume we have a function g that is both even and odd, then:

    g(-x) = g(x) = -g(-x) \Rightarrow g(-x) = -g(-x) \Rightarrow 2g(-x) = 0

    \Rightarrow g(x) \equiv 0
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