Is the product of an odd function and an even function odd or even?

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Answer 1 · 2015-11-14T11:12:27

odd

Suppose #f(x)# is odd and #g(x)# is even.

Then #f(-x) = -f(x)# and #g(-x) = g(x)# for all #x#

Let #h(x) = f(x)g(x)#

Then:

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

for all #x#

That is #h(x)# is odd.