So I am confused on this problem for my discrete math class, I didn't know if there was a specific formula you were supposed to use or what. The question is "What is the largest n for which one can solve within one second a problem using an algorithm that requires f(n) bit operations, where each bit operation is carried out in 10^-6 seconds, with these functions?
I think you're just supposed to use the information they've given you. You don't have to come up with anything fancy. Since each operation takes 10^(-6) = 0.000001 = 1/100,000 seconds, then you can't do more than 100,000 operations, no matter what. That's your cap.
a. f(n)= n^3
This says that you need n^3 operations for this particular problem ("f"). Since you can't do more than 100,000 operations, then n^3 <= 100,000. So what is n? Do the same thing for the other parts, too.