Final answer:
To calculate (f - g)(8) for the given functions f(x) = - |x| and g(x) = 1/2 * x - 9, find f(8) and g(8) and then take the difference. However, the resulting value -3 isn't among the provided options, indicating a possible mistake in the question.
Step-by-step explanation:
The question asks us to find the value of the expression (f - g)(8), where the functions f and g are defined as follows:
- f(x) = - |x|
- g(x) = 1/2 * x - 9
To find (f - g)(8), we first evaluate both functions at x = 8 and then subtract the value of g(8) from f(8).
First, find f(8):
f(8) = - |8| = -8
Next, find g(8):
g(8) = 1/2 * 8 - 9 = 4 - 9 = -5
Finally, subtract g(8) from f(8) to find (f - g)(8):
(f - g)(8) = f(8) - g(8) = (-8) - (-5) = -8 + 5 = -3
However, the answer -3 is not among the options provided. Therefore, it seems there might be an error in the question or the options presented.