Math Help - Determine whether x^3 is O(g(x)) for each of these functions g(x).

1. Determine whether x^3 is O(g(x)) for each of these functions g(x).

Code:
Determine whether x^3 is O(g(x)) for each of these functions g(x).

d) g(x) = x2 + x4
e) g(x) = 3x
f) g(x) = x3/2
d) Yes
e) Yes
f) No

Are my answers correct? I took the problem to mean that g(x) < c * x3.

2. Re: Determine whether x^3 is O(g(x)) for each of these functions g(x).

Hey lamentofking.

I think you have it the other way around. 3^x is an exponential function with infinite numbers of positive powered terms and x^4 has a term higher than x^3. f should be correct (i.e. yes).

3. Re: Determine whether x^3 is O(g(x)) for each of these functions g(x).

Originally Posted by lamentofking
Determine whether x^3 is O(g(x)) for each of these functions g(x).

I took the problem to mean that g(x) < c * x3.
No, it means that eventually x3 < c * g(x).

4. Re: Determine whether x^3 is O(g(x)) for each of these functions g(x).

Originally Posted by emakarov
No, it means that eventually x3 < c * g(x).
So then in terms of the question d), e), and f) are all yes? I thought f) would be no because if x3 < c * g(x) and (x^3)/2 means (1/2)x^3 with c=1/2 then x^3 would be greater than (>) c* g(x).

5. Re: Determine whether x^3 is O(g(x)) for each of these functions g(x).

Originally Posted by lamentofking
So then in terms of the question d), e), and f) are all yes?
Yes.

Originally Posted by lamentofking
I thought f) would be no because if x3 < c * g(x) and (x^3)/2 means (1/2)x^3 with c=1/2 then x^3 would be greater than (>) c* g(x).
Could you please re-formulate this clearly? "If x^3 < c * g(x)" eventually, then x^3 = O(g(x)), nothing more to prove. Are you sure you are assuming x^3 < c * g(x)? Next, by c * g(x) do you mean (1/4)x^3 since c = 1/2 and g(x) = (1/2)x^3? That's possible, but why not consider c = 1? Your quote above is not very clear.