Asymptotic Notation

Question

Assume that f(n) and g(n) are two functions, such that f(n)=O(g(n)). Which of the following always hold?

A)$f(n)=O((f(n))^{2})$

B)$f(n)=\Omega ((f(n))^{2})$

C)$g(n)=O ((f(n))^{2})$

D)$g(n)=\Omega (g(n))$

Comments

Take f(n) = 1/n  this will eleminate option (a).

and f(n) = n this will eleminate option (b)

and f(n) = n and g(n) = n⁴  will eliminate (c)

option D always true. 

---

i didn't get u. Can u plz elloborate it for option a

---

@$ruthi problem with option A is when f(n) = 1/n then it cannot be O(f(n^2)) because square of 1/n will always be larger than 1/n 

for example: f(n) = n

f(1/2) = 1/2

f(1/4) = 1/4
 

f(1/2) = O(f(n^2)) 
1/2 = O(1/4) // this does not hold