Let V be the vector space of continuous real-valued functions on the interval [−1,1] of the real line. Let We be the subspace of even functions, f(−x)=f(x), and let Wo be the subspace of odd functions, f(−x)=−f(x).
(a) Show that V=We⊕Wo.
(b) If T is the indefinite integral operator
(Tf)(x)=∫0xf(t)dt
are We and Wo invariant under T?