For any x∈(-a, a)

∵f(x) and g(x) are odd function and even functions on (-a, a) respectively.

∴f(-x)=-f(x)

g(-x)=g(x)

∴f(-x)=f(-x)*g(-x)=-f(x)*g(x)=-f(x)

∴F(x) is the odd function on (-a, a).

That is, f(x)*g(x) is the odd function on (-a, a).