Question 42

The value of f(-2) + f(-3) is 6.

To calculate f(-2) + f(-3), we first evaluate f at both points. For f(-2), since -2 is equal to -2, we use the second part of the function, yielding f(-2) = (-2)² - 1 = 4 - 1 = 3. For f(-3), which is less than -2, we use the first part of the function, giving f(-3) = -3 + 6 = 3. Therefore, f(-2) + f(-3) = 3 + 3 = 6.

A) -5

This option is incorrect because f(-2) + f(-3) evaluates to 6, not -5. The calculations show that both function values yield positive results, directly contradicting this option.

B) 6

This option is correct. The evaluation of f(-2) gives 3 and f(-3) also gives 3, leading to a sum of 6. This matches the calculations based on the defined function.

C) 7

This option is incorrect as it does not align with the calculated sum of f(-2) and f(-3). The correct evaluation leads to a total of 6, not 7.

D) 11

This option is also incorrect. The functions evaluated at the given points do not provide a sum that reaches 11. The calculations confirm a total of 6, thereby disqualifying this option.

E) 18

This option is incorrect. The computed values of f(-2) and f(-3) do not sum to 18. The total derived from the evaluations is 6, clearly dismissing this choice.

Conclusion

The correct response is 6 because it accurately reflects the sum of the function values at the specified points. All other options fail to match the calculations derived from the defined function, confirming their incorrectness. The evaluations demonstrate a clear understanding of how to apply piecewise functions to find specific values.