Consider the following function complexities
f1(n) = 5n2-n+3 f2(n) = 5lgn + 3 f3(n) = 4nlgn
f4(n) = 3n + 4 f5(n) = lg(n2) f6(n) = en
(a) List all the elements of the following Big “O” sets, given the following 5 functions. Remember that Big “O” contains proportional and slower-growing functions. All you need to do is add all appropriate fi into the sets, denoted by the { }. It is possible that a set will not have elements in it.
O(n3) = { }
O(n) = { }
O(lgn) = { }
O(3n) = { }
(b) Do the same for the Big \theta and Little “o” sets. It is possible that a set will not have elements in it.
\theta (n2) = { }
\theta (lgn) = { }
o(nlgn) = { }
o(3n) = { }
(c) If Suppose f(n) is a function which belongs in sets O(n2) as well as in \Omega (n). List any 4 functions that would belong in both sets.
________, ________, ________, ________
(d) Suppose a function f(n) belongs in both O(g(n)) and \Omega (g(n)). Clearly explain why this function also must belong in \theta (g(n)).