option A will be correct
In order to find the order of the algorithm, there are three possible cases with f(n) and g(n)
Case-1 : if f(n) > g(n)
In this case we take O(f(n)) the complexity of the algorithm as g(n) is a lower order term, we can ignore this one .
Case-2 : f(n) < g(n)
In this case we take O(g(n)) the complexity of the algorithm as f(n) is a lower order term, we can ignore this one.
Case-3: f(n) = g(n)
Time Complexity can be either O(g(n)) or O(f(n)) (which is equal asymptotically). So the order of the algorithm is max(f(n), g(n))