Answer :
Final answer:
The values of the function f(x) at -1, 1, and 2 are 5, 9, and 8, respectively. Summing these values yields d) 22, which is the answer to the student's question.
Explanation:
The student has asked to evaluate the function f(x) = |x²-2x-8| at three different values of x: -1, 1, and 2, and then to sum these values. To solve this, we need to first calculate the value of the function at each specified x, and then add them together.
For f(-1), we substitute x with -1: |(-1)² - 2(-1) - 8| = |1 + 2 - 8| = |-5| = 5.
For f(1), we substitute x with 1: |(1)² - 2(1) - 8| = |1 - 2 - 8| = |-9| = 9.
For f(2), we substitute x with 2: |(2)² - 2(2) - 8| = |4 - 4 - 8| = |-8| = 8.
Now, we sum up these values: 5 + 9 + 8 = 22. Therefore, the value of f(-1) + f(1) + f(2) is 22.
