Question 11

g(-3) equals 1.

To find the value of g(-3), we first need to evaluate g(x) using the function definition g(x) = f(-x). Therefore, g(-3) = f(3). Next, we substitute 3 into the function f(x) = (x - 3)^2 + 1, which results in f(3) = (3 - 3)^2 + 1 = 0 + 1 = 1.

A) 1

Option A is correct because, as calculated, g(-3) = f(3) = 1. This aligns perfectly with the function definition provided and the arithmetic performed.

B) 4

Option B is incorrect because substituting x = 3 into the function f(x) does not yield 4. The correct value calculated from f(3) is 1, not 4, indicating a misunderstanding of the function's evaluation.

C) 7

Option C is incorrect as well. The function f(x) evaluated at x = 3 results in 1, not 7. This choice misrepresents the result of f(3) and does not reflect the function's behavior.

D) 10

Option D is also incorrect. There is no calculation or substitution within the function f(x) that would lead to a result of 10 when x is substituted with 3. The correct evaluation shows a result of 1.

Conclusion

The correct answer is definitively A) 1, as it is the only option correctly derived from the function evaluations. All other options misinterpret the calculation and do not align with the definition of the function g(x) based on f(x).