Final answer:
The student's question is incomplete as it lacks the necessary functions s(x) and g(f(x)) to determine function J. The provided options suggest J is a quadratic function, and solving for it would typically involve analyzing equations of the form ax²+bx+c=0, but we can't proceed without additional information.
Step-by-step explanation:
The question "Which formula will define function J if s(x) - g (f (x))" seems to involve the composition of functions, where one function is subtracted from another. To find function J, we would need to have explicit forms for s(x) and g(f(x)). However, as the necessary details are not provided in the student's question, we cannot definitively choose between the options A, B, or C given for J(x) without additional information.
It is also suggested through the information that you have provided, such as "ax²+bx+c = 0", that a quadratic equation is considered, with potential application of the quadratic formula for finding roots or analyzing function behavior. Without the explicit definition of s(x) and g(f(x)), we cannot determine which of the options for J(x) would accurately represent the combination of the functions involved.