Let V = Cn(R) be the vector space consisting of all continuous functions f: R R.

Question:

Let V = Cn(R) be the vector space consisting of all continuous functions f: R → R. Explain why the set of all functions such that f(1) = 0 forms a subspace, but the set of functions such that f(0) = 1 does not. For which values of a, b does the set of functions such that f(a) = b form a subspace?