If f(n) = θ(g(n)) and g(n) = O(h(n)), then which of the following is true?

Explanation

f(n) = θ(g(n)) means f(n) is both O(g(n)) and Ω(g(n)); in particular f(n) = O(g(n)). Combined with the given g(n) = O(h(n)), the transitivity of O-notation gives f(n) = O(g(n)) = O(h(n)), so f(n) = O(h(n)). Only an upper bound relating g and h is given, with no information about a matching lower bound, so none of f(n)=θ(h(n)), h(n)=O(f(n)) or h(n)=θ(f(n)) can be concluded in general. Hence the statement guaranteed to be true is f(n) = O(h(n)).