express the function in Ω-notation

[user4592357]

i'm learning algorithm analysis, about the different notations, and in class we wrote an example:

f(n) = 1/2*n^2 + 3n,

and wrote it using O-notation, Ω-notation and Θ-notation:

T(n) = Ω(n)
T(n) = O(n^2)
T(n) = Θ(n^2)

now i'm reading the book, where it says f(n) = Θ(g(n)) is true if and only if both f(n) = O(g(n)) and f(n) = Ω(g(n)) are correct.

in the example we wrote, it says T(n) = Θ(n^2) (which i do agree with) which means both T(n) = O(n^2) and T(n) = Ω(n^2) should hold. but we wrote T(n) = Ω(n). i think that's incorrect? (we wrote that because of the term 3n which means that at least 3n operations are done)

i think it should be T(n) = Ω(n^2) instead of Ω(n)

please correct me if i'm wrong. thanks in advance