(1) Consider the function f(x) = 3x5 + 5x3 + 1000. Identify whether each of the following statements is true or false and briefly but precisely justify your answer (using the definitions of O(), 60,22()). (a) f(n) is in O(n8). (b) f(n) is in O(n5). (c) f(n) is in O(n^). (d) f(n) is in O(n8). (e) f(n) is in O(n5). (f) f(n) is in Q(n)