i need solutions a , c and d

Problem #4 (20 points) Establish a big-O relationship by finding witnesses and k such that f(x) g(x)| whenever x > k. (a) Determine whether each of these functions is 0(x). (1) f(x) = 10 (ii) f(x) = 3x + 7 (iii) (x) = x2 + x + 1 (b) Determine whether each of these functions is 0(). (1) f(x) = 17x + 11 (ii) S(x) = x2 + 1000 (iii)/(x) = x log.x (c) Use the definition of "f(x) is O(g(x))" to show that x4 + 9x2 + 4x + 7 is 0(x). (d) 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. 1:0 for i:=1 to 3 for i:=1 to 4 1:31+ ij (e) Give a big-O estimate for the number additions used in this segment of an algorithm. 1:=0 for i:=1 to n for i:=1 ton 1:=t+i+i