SOLUTION: Prove that the product of two odd functions is an even function.

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Question 1089954: Prove that the product of two odd functions is an even function.
Answer by math_helper(2461) About Me  (Show Source):
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Let g(x) and h(x) both be ODD functions.
Then g(-x) = -g(x) for all x in the domain of g(x)
and h(-x) = -h(x) for all x in the domain of h(x)
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Let's see what happens when we multiply g(-x) by h(-x):
g(-x)*h(-x) = (-g(x))*(-h(x)) = g(x)*h(x)
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If we let a(x) = the product g(x)*h(x) we see that a(-x) = a(x) for all x in domain of a(x), which fits the definition of an EVEN function.