Thread: Prove even functions set is a vector space

Prove that set of even functions under addition and scalar multiplication is a vector space.

Proof. Let F denote the set of functions f with f(t) = f(-t) for all t.

Now let f and g be in F, then (f+g) (t) = f(t) + g(t), (fog)(t) = f(g(t)).

Is that enough to prove that it is a vector space?

Originally Posted by tttcomrader

Prove that set of even functions under addition and scalar multiplication is a vector space.

Proof. Let F denote the set of functions f with f(t) = f(-t) for all t.

Now let f and g be in F, then (f+g) (t) = f(t) + g(t), (fog)(t) = f(g(t)).

Is that enough to prove that it is a vector space?

If are even then is even and is even where . So it is a vector space.