If $f(x) = \Omega(n)$ and $g(x)= O(n)$, what would be the order of growth of $f(x) \cdot g(x)$ ?
First I figured it should $\Theta(n)$ , as two extremes would cancel each other and the order of growth will be same as $n$
But, where I came across this question, the answer given was $\Omega(n)$, and no proof was mentioned. Well, I didn't understand why, but intuitively I convinced myself as "you can't know for sure the upper limit of growth for $f(x) \cdot g(x)$ so you can't say it's $O(n)$, but you can be sure that it won't be lower than $\Omega(n)$"
Can someone help me in understanding this, in a more believable way?