Let V be the set of all complex-valued functions f on the real line such that (for all t in R)
f(−t)=f(t).
The bar denotes complex conjugation. Show that V, with the operations
(f+g)(t)=f(t)+g(t)(cf)(t)=cf(t)
is a vector space over the field of real numbers. Give an example of a function in V which is not real-valued.