Java

stion 4 (20%) You are given the following definitions for your convenience. 0(g(n)) = {f(n) : there exist positive constants c and no such that (g(n)) = {f(n) : there exist positive constants c and no such that 6(g(n)) = {f(n) : there exist positive constants c1, c2, and no such that (a) Using that definition, prove that T(n)-4n2 + 2n + 1 e (n2) (10 points) 0 s f(n) s cg(n) for all n 2 no). 0 cg(n)s f(n) for all no) . 0 S cig(n) S (n) s cag(n) for all n no).1 (b) Is O(n3) a tight upper bound for T(n)? If not, what is the tight upper bound for T(n)? (10 points)