1. Find two strictly increasing functions f(n) and g(n) such that f(n) O(g(n)) and g(n) g o(f(n)), and both involving only "elementary" operations in their description. For instance, exponentials and factorials are OK, Tibor Rado's so-called "Busy Beaver" functions are not (Google if you don't know what these functions are, but they are not needed for the resolution of this exercise anyway). Prove that the functions you found do indeed satisfy the above relationships (pay particular attention to the requirement that the functions are strictly increasing, e.g. f (n) - sinn and g(n)cosn trivially fail to satisfy this requirement)