Final answer:
To satisfy the equation f(x) × g(x) = 0, where f(x) is a constant function and g(x) is a linear function with a non-zero slope, f(x) must be equal to zero.
Step-by-step explanation:
The student is asked to determine f(x) given that f(x) is a constant function and f(x) × g(x) = 0 where g(x) = 5x + 6. Since the only way for a product to be zero is if at least one of the factors is zero and f(x) is constant, meaning its value does not depend on x, f(x) must be 0 to satisfy the equation regardless of the value of g(x).
To summarize, the constant function f(x) that would satisfy the equation f(x) × g(x) = 0 when g(x) is a linear function with a non-zero slope (in this case 5) and an intercept (in this case 6), is f(x) = 0.