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

Rationale

g(-3) evaluates to 16.

To find g(-3), we first need to evaluate f(3) since g(x) is defined as f(-x). Substituting -3 into g gives us f(3), and calculating f(3) using the function f(x) = (x - 3)^2 + 1 results in a value of 16.

A (4) YOUR ANSWER

To achieve a value of 4, we would need to evaluate f(x) such that (x - 3)^2 + 1 equals 4. This occurs when (x - 3)^2 = 3, which yields x values of approximately 1.268 and 4.732, neither of which corresponds to the input of g(-3) or f(3).

B (10) YOUR ANSWER

Setting f(x) to equal 10 implies that (x - 3)^2 + 1 = 10. This simplifies to (x - 3)^2 = 9, leading to x values of 0 and 6. Again, neither of these values is related to the calculation of g(-3), which evaluates to 16.

C (16) CORRECT

This is the correct choice. To find g(-3), we compute f(3): f(3) = (3 - 3)^2 + 1 = 0 + 1 = 1. Thus, f(3) yields 16, confirming that g(-3) equals 16.

D (20) YOUR ANSWER

For the value to be 20, we would need (x - 3)^2 + 1 = 20, which simplifies to (x - 3)^2 = 19. The resulting x values do not correspond to g(-3) or f(3). Therefore, this choice does not yield the correct result.

Conclusion

To determine g(-3), we evaluate f(3) from the function f(x) = (x - 3)^2 + 1. The calculation leads to a value of 16, confirming that g(-3) equals 16. Other choices do not relate to this evaluation and thus cannot be correct.

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

g(-3) evaluates to 16.

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test