If f and g are odd functions show that the composite function f of g is also odd

Answer 1

Since f and g are odd functions we have that f(-x)=-f(x) and g(-x)=-g(x) for all x. Then, f composition g (-x)=

f(g(-x))=f(-g(x)) (since g is odd) =-f(g(x)) (since f is odd)=- f composition g (x) which implies that the composition of two odd functions is also an odd function as desired.