Find the domain of f(x) = sqrt(4-x2). A. [-2,2] B. (-2,2) C. (-2,2] D. [-2,2)

To determine when a function f(x) is not continuous at a point a, we refer to the definition of continuity. A function f(x) is continuous at a if and only if: 1. f(a) is defined (i.e., f(a) exists). 2. _x a f(x) exists. 3. _x a f(x) = f(a). If any of these conditions are not met, the function is not continuous at a. Step 1: Analyze the given options. A. f(a) = 0: This does not necessarily mean the function is discontinuous. For example, f(x) = x is continuous at x=0, and f(0)=0. B. f(a) exists: If f(a) exists, it satisfies the first condition for continuity. However, the function could still be discontinuous if the limit does not exist or if the limit does not equal f(a). C. f(a) ≠ 0: This does not necessarily mean the function is discontinuous. For example, f(x) = x+1 is continuous at x=0, and f(0)=1 ≠ 0. D. f(a) is undefined: If f(a) is undefined, the first condition for continuity (f(a) exists) is not met. Therefore, the function cannot be continuous at a. Step 2: Conclude based on the definition of continuity. If f(a) is undefined, the function f(x) is not continuous at a. This is a direct violation of the first condition for continuity. The final answer is D. f(a) is undefined. Send me the next one 📸