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(−¡Þ, ¡Þ).

Question

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(−¡Þ, ¡Þ).

Which of the following subsets are subspaces of the vector space C(−¡Þ, ¡Þ)? (Note: Calculus is required to complete this exercise.)

(a) All nonnegative functions
(b) All constant functions