What notation is used to discuss the coefficients of functions in big-O notation?
I have two functions:
- $f(x) = 7x^2 + 4x +2$
- $g(x) = 3x^2 + 5x +4$
Obviously, both functions are $O(x^2)$, indeed $\Theta(x^2)$, but that doesn't allow a comparison further than that. How do I discuss the the coefficients 7 and 3. Reducing the coefficient to 3 doesn't change the asymptotic complexity but it still makes a significant difference to runtime/memory usage.
Is it wrong to say that $f$ is $O(7x^2)$ and $g$ is $O(3x^2)$ ? Is there other notation that does take coefficients into consideration? Or what would be the best way to discuss this?