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

• 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. $f(a) \neq 0$: This does not necessarily mean the function is discontinuous. For example, $f(x) = x+1$ is continuous at $x=0$, and $f(0)=1 \neq 0$.
• 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 $a$.

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 $\boxed{\text{D. } f(a) \text{ is undefined}}$.