Select a theta notation for f(n) + g(n)
f(n) = 6n^3+2n^2+4, g(n) = Θ(n ln n
Would the theta notation be Θ(n^3) or Θ(n^k)?
What is k? Are you claiming that f(n) + g(n) = Θ(n^k) for some k? This is true, but it certainly carries less information that saying that f(n) + g(n) = Θ(n^3). Whether you are allowed to use such non-specific answer depends on the problem and course requirements. You could as well say that f(n) + g(n) = Θ(f(n) + g(n)) or f(n) + g(n) = Θ(h(n)) for some h; that would be correct but carry no information at all.
The correct answer is probably Θ(n^3).