multiplying 2 functions that are both big O of a third
<p>Having an issue with a homework problem. Question asks if <code>f(n) = O(h(n))</code> and <code>g(n) = O(h(n))</code> then <code>f(n) * g(n) = O(h(n))</code> is a true statement.</p>

<p>I have been researching and the best answer I can come up with is that it is true but not all of the time. I can come up with examples where it is true but I am having issues coming up with a case where it is false. Can anyone give me such an example or at least direct me to a link that is relevant to my question? Any help would be greatly appreciated.</p>