Complexity analysis after multiplying two functions

Question

Given F (n) = θ (n)

H (n) = O (n)

G (n) = Ω (n)

then what is the order of F (n) + [G (n). H (n)]?

edit: F (n) = θ (n) not Q (n)

Answer 1

, - P(n) = G(n)*H(n). , , , G , , ; , , . , , H ; . P(n) , , F(n) + P(n) .

, , , H(n) = Ω(1) (.., , ). P(n):

P(n) = H(n) * G(n)
     >= C1 * G(n)
     = Ω(G(n)) = Ω(n)

P(n) <= C1*n * G(n)
      = O(n*G(n))

, F(n) + P(n) = Ω(n) F(n) + P(n) = O(n*G(n)), ; , H G.