Can you thoroughly show me how to do problem one?

1. Disprove the following statement If f(n) is a positive function then f (n) = O (f (n-1)) Hint: consider some fast growing function 2. Give a -bound for the solution of the following recurrence: T(n) = 7.2(2) + 3. Given an array A of size n, does the following code produce a uniform random permutation? Please explain for i 1 to n - 1 swap Ali] with A[RAN DOM(i +1,n) 4. Show the operation of HEAPSORT on the array A=(7, 4, 5, 8, 1,9), starting with BUILD-MAX-HEAP and continuing with the first call of MAX-HEAPIFY after that. of n elements, we would like to find the k largest elements ed order, using the following approach. Use an efficient selection 5. Given a set in sort algorithm to find the k'th largest element, partition with respect to that element, and then sort the k largest elements. Determine the worst-case number of comparisons of the resulting algo- rithm in terms of n and k. For what values of k do we get a linear time algorithm