If f, g are odd real functions, then their composition is an odd real function Proof

Functions are provided
Prove that:
a) If f, g are odd real functions, then their composition is an odd real function

Proof
f(-x)=-f(x) , for every x in R
g(-x)=-g(x),for every x in R

(f*g)(-x)=f(g(-x))=f(-(g(x))=-f(g(x))=-(f*g)(x)