Let f be the function defined by f( n) = n^3 for each nN. For which of the following functions g is f( n) = O(g(n))?

a) g(n) = n^2 + 1.

b) g(n) = n^3 + 1.

c) g(n) = 1/2 n^3 .

d) g(n) = 1/2 n^4 .

e) g(n) = 2^n .

f) g(n) = n^2 log n.

Let f be the function defined by f(n) = ns for each n N. For which of the following functions g is f(n) 0(g(n))? (a) g(n)-n2+1. (b) g(n)=n3+1. (c) g(n)=n3. (d) g(n)=h'. (e) g(n)=2". (f) g(n)=n2 logn