A function f : R → R is called even if f(−x) = f(x) for all x ∈ R, and it’s called odd if f(−x) = −f(x) for all x ∈ R. LetV =Fun(R,R)be the set of all functions f:R→R,and let E,O⊂V denote the subsets of even and odd functions from R to R, respectively.
(i) Show that E and O are subspaces of Fun(R, R).
(ii) Show that E ∩ O = {0}.
Hint: 0 is the only number that is equal to its negative.