Question

Does the multiplication of two odd functions always result in an even one?

Answer 1

Yep

Answer 2

Is there a proof for this question?

Answer 3

Let f(x) and g(x) be odd functions

By definition, this means


f(-x) = -f(x)

g(-x) = -g(x)


for all defined values in the domains of f and g.



Now let h(x) be the product of these odd functions to get


h(x) = f(x)*g(x)


Now, replace each "x" with "-x" and simplify


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


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


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


h(-x) = h(x)


So this shows that h(x) is now an even function

Answer 4

what about f(x) = 3x^3 times g(x) = 4x^3
wouldn't it be 12x^9, an odd function?

Answer 5

you add the exponents, not multiply them

Answer 6

so for monomials, adding two odd exponents will give you an even exponent every time

Answer 7

My bad, i suppose that the odd functions will always be even when multiplied

Answer 8

yes and it's proven above