I am confused on defining the function f(n) using another function
Don't be confused, it's actually pretty simple. The big O notation is an inequation. That means that we can find multiple upper bounds for f(n) and still be correct, hence, although we can write f(n) = O(f(n)) and be correct it's, depending on f(n), often not what we are intending to express.
It's a measure of growth rates. f(n) = 2n does not grow faster than f(n) = n. Both growths are linear.
f(n) = O(n*f(n))
I'll assume you meant the second n to be a constant c.
By definition of Big O, this constant is already in the inequation. So when you write the Big O you're actually writing c * abs(g(x)). If you can find a constant factor you needn't mention it, because the definition of Big O, the inequation, already takes care of that.