Let V be the set of all real-valued continuous functions defined on R1. If f and g are in V, we define f ⊕ g by (f ⊕ g)(t) = f(t) + g(t). If f is in V and c is a scalar, we define c f by (c f)(t) = cf(t). Then V is a vector space, which is denoted by C(−∞, ∞).

Question

Which of the following subsets are subspaces of the vector space C(−∞, ∞)? (Note: Calculus is required to complete this exercise.)
(a) All nonnegative functions

b) all constant functions
c)All functions f such that f(0) = 0

how do ido this

Answer 1

(a) Nope
if f(t) >= 0 but c < 0, cf(t) is not a nonnegative function

Looks to me like (b) and (c) are both subspaces. Do we have to choose only one?