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).