Final answer:
The proper quotient and remainder of the functions f(x) and g(x) cannot be determined due to the inaccurate representation of f(x) in the question. Correct polynomial long division requires a well-defined polynomial f(x), which is missing here.
Step-by-step explanation:
To determine the quotient of the functions f and g, where f(x) is a polynomial and g(x) = x² + 3, we would perform polynomial long division. However, the functions are not properly defined in the question. Assuming that f(x) is meant to be a polynomial in terms of x, the quotient q(x) and remainder r when f(x) is divided by g(x) are not clearly provided due to the errors in the question itself. Hence, we cannot determine the quotient and remainder without the correct form of f(x).
If correctly given, the calculation would involve dividing the leading terms and then using subtraction and repeated division until the degree of the remainder is less than the degree of g(x), thus obtaining q(x) and r. For example, if f(x) were x´ + 2x³ - 5 and g(x) = x² + 3, the quotient q(x) would be x² + 2x minus a certain number and the remainder r would be a polynomial of degree 1 or less or a constant.