If f(n) = Θ(g(n)) then what all can one say about f(h(n)) and Θ(g(h(n)) I was going across some problems which translated the fact that $\log (n!) = \Theta(n\log n)$ to give
$$\log(\lceil\log n\rceil!) = \Theta(\lceil\log n\rceil \log \lceil\log n\rceil)$$
and therefore $\log(\lceil \log n\rceil!) =  \omega(\lg n)$.  

Now I just have this intuition that this sort of conversions shouldn't and wouldn't be always right.

Would it be right to think that.

Any justification as to why am I wrong in thinking that and guidance to what I should have a look at, what texts I should go through to understand it better for myself are very much appreciated. 

Thank you.
In general, you can prove nothing. You know $f(n) = \Theta(g(n))$. Now assume f (n) = g (n) = n for all n except g (n) = 0 if n ≤ 1000. And h (n) = 1000 for all n. 

So we now have f (h (n)) = 1000 and g (h (n)) = 0. 

The problem is that $O (n)$ and $\Theta (n)$ only work for large n. You are fine if h (n) -> inf, or if you look specifically at f (n) and h (n). 

If the limit of h (n) is infinity, then you overcome the problem that $\Theta(g(n))$ only gives you information for n ≥ N for some possibly large N, because h (n) will eventually be greater than that N.