Please explain Let fn 4n3 4n 4 Let gn 2n3 2n2 2 Select

Please explain.

Let f(n) = 4n^3 + 4n + 4 Let g(n) = 2n^3 + 2n^2 + 2 Select the first answer below that is true. f is (g) f is O (g) f is ohm (g)

Solution

if n=1 f(1) = 4* 1³ +4*1 + 4=12,

g(1) = 2*1³ + 2*1² + 2 = 6

if n=2 f(2) = 4*2³ + 4*2 + 4 = 44

g(2) = 2*2³ + 2*2² + 2 = 26

Here always f(n)>c.g(n) So the answer is f is Big Omega of g.ie; last option.