3. [10 marks] Given two functions f(n) and g(n) such that f(n) = (g(n)), decide for each of the following statements whether it can be inferred from the fact that f(n) = (g(n)). Justify each answer, that is, prove the statement if your answer is yes, and provide a counterexample and argue why it is a counterexample if your answer is no.

(i) (f(n))^2 = ((g(n))^2).

(ii) 2^(f(n)) = (2^(g(n))).