2) [12 marks] Determine whether x is O(g(x)) for each of these functions gx). a) g(x)-x b) g(x)=x,x' c) g(r)-3 3) 8 marks] Find a C and k for big-O and plot the fx) and C.gfx) function for f(x)-2-3r+ 4 and g(x)-x2. Assume x>0 4 8 marks] Give a big-O estimate for the number of operations, where an operation is a comparison or a multiplication, used in this segment of an algorithm. Ignore comparisons used to test the conditions in the for loops (ai, az., an are positive real numbers) m: 0 fori1 to n for j ::: i + 1 to n m: max(axa, m) [10 marks] Give a big-O estimate for the number of operations, where an operation is an addition or a multiplication, used in this segment of an algorithm. Ignore comparisons used to test the conditions in the while loop while is n i-2x 6[6 marks] Suppose that an element is known to be among the first four elements in a sorted list of 64 elements. Would a linear search or a binary search locate this element more rapidly? Justify your