1. Let C[a,b] denote the set of all real-valued continuous functions on [a,b]. If g and f are in C[a,b], we define fog = f(t) +g(t) and cOf = cf(t) for all scalars c. a. Show that C[a,b] is a real vector space. b. Let Wx be the set of all functions in C[a,b] such that f(a) = k. For what values of k will Wk be a subspace of C[a,b]