Final answer:
The value of the expression f(x)+12 when x=8 is f(8)+12, and the probability P (0 < x < 12) for the given continuous probability function is 144.
Step-by-step explanation:
The value of f(x)+12 when the input, x, is equal to 8, is found by substituting 8 into the function f and then adding 12 to the result. Therefore, the value of f(x)+12 for x=8 is f(8)+12, which corresponds to option A) f(8)+12.
Regarding the continuous probability function where f(x) equals 12 and is restricted to the interval 0 ≤ x ≤ 12, we want to find the probability P (0 < x < 12). Since the probability function is constant and the interval is the entire defined range except for the endpoints, the probability is actually the integral of f(x) over the interval (0, 12). The value of the function f(x) is 12 for this interval. So, the probability is the product of the value of the function and the length of the interval without including the endpoints.
Therefore, P (0 < x < 12) = f(x) × (12 - 0) = 12 × 12 = 144.