I know that an odd function is fx fx and that an even funct

I know that an odd function is f(-x) = -f(x) and that an even function is f(x) = f(-x), but i dont understand how to apply it to this problem because its just a group of functions. How would I solve this problem step by step?

Solution

It depends on f and g
If f is odd and g is odd
h(-x)=f(g(-x))=f(-g(x))=-f(g(x))=-h(x) so h is odd
If f is even and g is odd
h(-x)=f(g(-x))=f(-g(x))=f(g(x))=h(x) so h is even
if f is odd and g even
h(-x)=f(g(-x))=f(g(x))=h(x) so h is even
if f is even and g is even ...I let you find