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college algebra

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Let f denote an odd function and g an odd function. Decide whether the function h(x)=g(x) f(x) is even or odd.

  • college algebra - ,

    h(-x) = f(-x)g(-x)

    f(-x) = -f(x)

    g(-x) = -g(x) ---->

    f(-x)g(-x) = f(x)g(x) = h(x)

    So:

    h(-x) = h(x)

  • college algebra - ,

    g(x)*f(x) is an even function, since both f and g change signs when x is replaced by -x

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