Let f (n) = Ο(n), g(n) = Ω(n) and h(n) = θ(n). Then g(n) + f(n).h(n) is ______ A.) Ω(n) B.) θ(n2) C.) Ω(n2) D.) θ(n) How to do these type of questions ?

what if i take f(x) = sinx, g(x)= cosx? these two cant be compared. sinx cant be written as O(cosx) and also cosx cant be written as O(sinx) then B becomes invalid. plz verify

Let $f(n)$ = Ω(n) and g(n) = O(f(n)). Then g(n) = _______ [Assume n>0 ] (a.) Ω(n) (b.) O(n) (c.) θ(n) (d.) Ω(1) According to me, the answer should be (b.) since, f(n) has lowest bound n and g(n) has f(n) as upper bound. Answer given is (d.) I am confused about the answer.