Let C(R) be the vector space of continuous functions from R to Rwith the usual addition and scalar multiplication. Determine if Wis a subspace of C(R). Show algebraically and explain your answersthoroughly.
a. W = C^n(R) = { f ∈ C(R) | f has a continuous nthderivative}
b. W = {f ∈ C^2(R) | f''(x) + f(x) = 0}
c. W = {f ∈ C(R) | f(-x) = f(x)}.
