Let ORR) denote the space of all bounded, continuous functions f : R gt; (C. Let COOK) denote the set of continuous functions f : 1R ) (C for which...

Please help me prove the following question about the space of all bounded, continuous functions?

Let ORR) denote the space of all bounded, continuous functions f : R —> (C. Let COOK)denote the set of continuous functions f : 1R —) (C for which lim f(a:) = 0. msdzoo a) Prove that every f E ODOR) is bounded. b) Prove that ODOR) is closed in CAR) (equipped with the uniform metric d(f, g) :=5111336112 If (99) - g($)l-).