Question 11621 – Asymptotic-Complexity

g1(n) = {n3 for 0≤n<10,000 n2 for n≥10,000  
g2(n) = {n for 0≤n<100 n3 for n≥100  

Whenever we go for asymptotic complexity, we look for large value of n. So in the given question, for large value of n like n>=10000, g₁(n)=n² and g₂(n)=n³. So clearly g₁(n) is O(g₂(n)).