f(1)=f(2)==f(1000)=1 and for n>1000 f(n)=5n+f(n/1.01) Prove f(n)=O(n). Recall that x is the ceiling operator that returns the smallest integer at least x. Problem 4. Let f(n) be a function of positive integer n. We know: f(1)=1f(n)=10+2f(n/8). Prove f(n)=O(n1/3) Problem 5. Let f(n) be a function of positive integer n. We know: f(1)f(n)=1=f(n/4)+f(n/2)+n. Prove f(n)=O(n)