Final answer:
Option A. Without the explicit content of the options presented, it's impossible to determine which statement ensures the existence of f(3). Generally, for f(3) to exist, the function must be defined and continuous at x = 3, without discontinuities, and limits approaching from both sides must exist and be equal.
Step-by-step explanation:
To determine whether the function f(3) exists, we need to consider statements related to the existence and continuity of a function at a specific point. Regarding the options provided, without the explicit statements, it's challenging to give a precise answer, but we can discuss the general rules that would apply.
For f(3) to exist:
- The function must be defined at x = 3.
- There should be no discontinuities at x = 3 (e.g., holes, jumps, or asymptotes).
- Limits approaching x = 3 from both the left and the right should exist and be equal.
To evaluate the options, you would typically compare the details to these criteria. For instance, if an option indicates that the function is continuous and defined at x = 3, it would support the conclusion that f(3) exists. However, without the explicit content of the options, we cannot determine which statement is correct. Choices given might reference the continuity at a point, the evaluation of limits, or specific values indicating the existence of the function at x = 3.