Let g(x) = f(-x), where f(x) = (x - 3)^2 + 1. What is the value of g(-3)?

Rationale

g(-3) = 1.

To find the value of g(-3), we first need to evaluate f(3), as g(x) is defined as f(-x). By substituting -3 into g(x), we find g(-3) = f(3), which simplifies to (3 - 3)^2 + 1 = 1.

A (1) CORRECT

This choice correctly represents the value of g(-3). By calculating f(3) from the expression (3 - 3)^2 + 1, we find that it equals 1.

B (4) YOUR ANSWER

This choice is incorrect because it suggests that f(3) equals 4. However, substituting 3 into f(x) gives (3 - 3)^2 + 1 = 1, not 4.

C (7) YOUR ANSWER

This choice is also incorrect. If we were to find f(3) and mistakenly arrive at 7, we would be miscalculating the expression. The correct evaluation of f(3) is clearly 1.

D (10) YOUR ANSWER

This choice is incorrect as well, as it implies that f(3) equals 10. The computation (3 - 3)^2 + 1 clearly results in 1, not 10.

Conclusion

The function g(x) = f(-x) leads us to find g(-3) by evaluating f(3). As calculated, f(3) equals 1, making the correct answer A. All other options are based on incorrect evaluations of the function f(x). Understanding function transformations is crucial in obtaining accurate results in such problems.

Let g(x) = f(-x), where f(x) = (x - 3)^2 + 1. What is the value of g(-3)?

g(-3) = 1.

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