3. f is a function that satisfies the following: - f is in O(n'), - f is in Q(n), - f is neither in 0(n) nor in @(n2), but it can be represented with 0. Can you give an example of such a function f? Show that the function you name indeed satisfies all of the above. Also name a well-known algorithm that meets these conditions for all situations (best, worst and average cases). 4. For each pair of functions given below, point out the asymptotic relationships that apply: f = 0(g), f = 0(g), and f = 0(g). a. f(n) = nz and g(n) = logn b. f(n) = 1500 and g(n) = 2 c. f(n) = 800 . 2 and g(n) = 3n d. f(n) = 4n+13 and g(n) = 22n+2 e. f(n) = 9n . log n and g(n) = n . log in f. f(n) = n! and g(n) = (n + 1)