Are the realvalued odd functions closed under multipication

Are the real-valued odd functions closed under multipication?

I know the answer is yes, can you prove it?

Solution

Let f ,g be two real valued odd functions

f(-x)=-f(x). g(-x)=-g(x)

Now fg(-x)=f(g(-x))=f(-g(x))=-(fg(x)),g(x) in R

Hence it is closed under multiplication .