The function f is defined by f(x) = x+6, for x < - 2 and x²-1, for x >= - 2.
What is the value of f(- 2) + f(- 3) ?

Rationale

f(-2) + f(-3) equals 6.

To find the value of f(-2) + f(-3), we need to evaluate the function at both x = -2 and x = -3 based on the given piecewise definition. For x = -2, we use the formula for x >= -2, and for x = -3, we use the formula for x < -2. This results in f(-2) = 5 and f(-3) = 3, leading to a total of 6.

A (-5) YOUR ANSWER

Calculating f(-2) yields 5, and f(-3) yields 3, so their sum is 8, which does not match -5. Therefore, this option is incorrect.

B (6) CORRECT

For x = -2, we apply the formula for x >= -2: f(-2) = (-2)² - 1 = 3. For x = -3, we use the formula for x < -2: f(-3) = -3 + 6 = 3. Adding these, we find f(-2) + f(-3) = 3 + 3 = 6, confirming this is the correct answer.

C (7) YOUR ANSWER

With f(-2) = 5 and f(-3) = 3, their sum is 8, which does not correspond to 7. Thus, this choice is also incorrect.

D (11) YOUR ANSWER

Using the same calculations, f(-2) = 5 and f(-3) = 3, results in a total of 8. This does not match 11, making this option incorrect.

E (18) YOUR ANSWER

Once again, calculating f(-2) and f(-3) gives 5 and 3 respectively, leading to a total of 8. Therefore, this option is also incorrect.

Conclusion

The function f evaluated at x = -2 gives us 3, while at x = -3, it gives us 3 as well. When these values are summed, they yield a total of 6. Hence, the only correct choice is B, which accurately reflects the computed result for f(-2) + f(-3).

The function f is defined by f(x) = x+6, for x < - 2 and x²-1, for x >= - 2. What is the value of f(- 2) + f(- 3) ?

f(-2) + f(-3) equals 6.

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test

The function f is defined by f(x) = x+6, for x < - 2 and x²-1, for x >= - 2.
What is the value of f(- 2) + f(- 3) ?