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Math Help - Trig Proofs (Even, Odd, Neither)

  1. #1
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    Trig Proofs (Even, Odd, Neither)

    I need to write a proof showing that h(x) is either odd, even, or neither.

    Assume h(x) = f(x)*g(x) and f(x) is even and g(x) is odd.

    I think the first step would be substituting as follows: h(x)=f(-x)*-g(x) because of the def'n of even and odd functions.

    This is where I am stuck and don't know how to proceed.

    Any help is appreciated
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  2. #2
    Senior Member jakncoke's Avatar
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    Re: Trig Proofs (Even, Odd, Neither)

    A function is even if f(-x) = f(x)
    A function is odd if -f(x) = f(-x)
    Now, h(-x) = f(-x)g(-x)

    Now g(x) is odd, so g(-x) = -g(x)
    Now f(x) is even so f(-x) = f(x) ...

    so h(-x) = ...
    Last edited by jakncoke; November 18th 2012 at 07:35 PM.
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