We are given $f(x) = x^{x^2}$ and $g(x) = 2^{2^x}$. The question is to determine whether $f = O(g)$, $\Omega(g)$, or $\Theta(g)$. Because $f(x)$ and $g(x)$ intersect at $x=2$ and $f(x)$ grows faster than $g(x)$ after this point, is it correct to say that $f(x) = \Omega(g)$ as:
$$|f(x)| \ge C \cdot |g(x)|, \forall x > k$$
for some constants $C$ and $k$ where $C = 1$ and $k = 1$.