If $f(n)=n^a$ for a given $a>0$, find $g(n)$ such that $f(n)\notin O(g(n))$ and $f(n)\notin \Omega (g(n))$
For given $a&gt;0$ and $f(n)=n^a$ we consider
$$g(n)= \begin{cases}{}
n^{a+1}, &amp; n=2k\\ 
0, &amp; n=2k-1
\end{cases}$$
for $k\in \mathbb{N}$