Final answer:
Subtracting the function g(x) from f(x) gives (f-g)(x) = -x - 3. Evaluating g(-3) for g(x) = -2x² + 1 results in -17 (Option a).
Step-by-step explanation:
The question requires finding the function (f-g)(x) when given that f(x) = x - 4 and g(x) = 2x - 1. To do this, we need to subtract the second function from the first, that is f(x) - g(x), which results in (x - 4) - (2x - 1). Simplifying this expression, we combine like terms to get -x - 3 as the function for (f-g)(x).
The second part asks for the value of g(-3) when g(x) = -2x² + 1. Substituting -3 into the function for x gives us -2(-3)² + 1, which simplifies to -2(9) + 1 or -18 + 1. Therefore, the result is -17, which corresponds to option a.