[c-prog] Big-O Notation

[Nawlins Nightmare]

Here's my question:

"Assuming f(n) is O(g(n)) how do I prove that c is O(1)?"

I know that the theory of transivity says if f(n) is O(g(n)) and g(n) is 
O(h(n)), then f(n) if O(h(n)). Am I on the right track?