Final answer:
After evaluating the function g(x) at x = 9 and x = -14, and summing the results, the answer is 55/3 or 18±3. None of the provided options match this correct answer, which suggests there may be an error in the question options.
Step-by-step explanation:
To find the answer, we need to evaluate the function g(x) = 14 - (2/3)x at the given points x = 9 and x = -14, then sum the results. Let's start by evaluating g(9):
g(9) = 14 - (2/3)(9) = 14 - 6 = 8.
Next, let's evaluate g(-14):
g(-14) = 14 - (2/3)(-14) = 14 + (2/3)(14) = 14 + 28/3 = 14 + 9±3 = 23±3 = 31/3.
Now, adding g(9) and g(-14) gives us:
g(9) + g(-14) = 8 + 31/3 = 24/3 + 31/3 = 55/3.
The sum in its simplified form is 55/3, which, when converted to a whole number, is 18±3. Therefore, none of the options given (Option 1: -6, Option 2: 23, Option 3: 31, Option 4: -27) match the correct answer. It seems there may have been a mistake in the options provided.