For each part, suppose the functions f(n) and g(n) are asymptotically positive, as defined in Chapter 3 (page 45). Note that for a disproof, you should give a counterexample.

4(a). Prove or disprove: if f(n)=O(g(n)), then 2^f(n)=O(2^g(n)).

4(b). Prove or disprove: f(n) is O(f²(n)).

4(c). Say function f is "asymptotically non-decreasing" if f(n)f(n+1) for all large enough n. Prove or disprove: if f(n)=(n²), then f is asymptotically non-decreasing