Asymptotic Analysis For each of the following statements, decide whether it is always true, never true, or sometimes true for asymptotically nonnegative functions f and g. If it is always true or never true, give a proof. If it is sometimes true, give one example for which itis true, and one for which it is false.

(a) f(n) + g(n) = (max(f(n), g(n)))

(b) f(n) = (g(n)) and f(n) = O(g(n))

(c) f(n) = O(g(n)) implies 2^f(n) = O(2^g(n))