If f and g are even real functions , then their composition is an even real function

Prove that:
a) If f and g are  even real functions , then their composition is an even 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)