Consider f(n) = 3n² + 4n3, mathematically show that f(n) is O(n²), (n² ), and (n²).

For finding an item in a sorted array, consider tertiary search, which is similar to binary search. It compares array elements at two locations and elminiates 2/3 of the array. To analyze the number of comparisons, the recurrence equations are T(n) = 2 + T(n/3), T(2) = 2, and T(1) = 1, where n is the size of the array. Explain why the equations characterize tertiary search and solve for T(n).