Question about asymptotic analysis comparing two functions

I'd be glad for an explanation on the analysis of this exercise. Given these functions: $$f(n) = n^2 \\ g(n) = n^{2/3}$$

Show that $$f(n) = O(g(n))$$, or $$f(n) = \Omega(g(n))$$ and comment if $$f(n) = \Theta(g(n))$$

In my answer, it is $$\Theta(g(n))$$ with $$n_0 = 1, C = 1$$

PS: The exercise requires a mathematical demonstration of the answer.

• It looks incorrect. can you please add more details as to how you got this answer? Feb 20, 2020 at 19:24
• For instance: $n^{1/2} \leq C * n^{2/3} => \frac{n^{1/2}}{n^{2/3}} \leq C$. If we replace the variables with $1$, the assumption is satisfied. Feb 20, 2020 at 19:31
• Same goes to $\Omega$ Feb 20, 2020 at 19:31
• Please recheck the definitions of $\Omega, \Theta, O$ especially about the condition of n’s that you have to choose. Feb 20, 2020 at 19:33
• $\Omega$ means that there is a function multiplied by a constant that is $\leq$ than $f(n)$ for an existing $n_0, C$. $O$ is the upper bound and $\Theta$ means that there is both boundaries. Feb 20, 2020 at 19:36