part b and e please ,show me all steps and good hand writing thank you ..

(discrete structurs)

Problem #3 (20 points) Establish a big-O relationship by finding witnesses C and k such that f (x)l (a) Determine whether each of these functions is O() Cgx) whenever x>k (i),f(x) 10 (ii).f(x)-3x + 7 (iii),f(x)-x2 + x + 1 (b) Determine whether each of these functions is O (i),f(x) = 17x + 1 1 (ii),f(x) = X2 + 1000 (iii).f(x) = x log x (c) Use the definition of"f(X) is O(g(v)" to show thats' + 9r' + 4x + 7 is O( (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. for to 3 forj to 4 +ij (e) Give a big-O estimate for the number additions used in this segment of an algorithm fori 1 to n forj to n