I think i got this right, not sure. Please check for me.

Let f: R--->R be given by

f(x)=4x^3 - 3x^2 +1

Prove from first principles, that f(x)= O(x^3)

f(x)=4x^3 - 3x^2 +1

<=4x^3 -3x^3 + x^3=2x^3

So, does me saying f(x)<=2g(x^3) provide proof? or is there something else i have to do?