Let $X=\{x \in \mathbb{R} \mid x \neq-3\}$. Let $f: X \rightarrow \mathbb{R}$ be a function defined as
$f(x)= \begin{cases}\frac{x^3-27}{x^2-9} & \text { if } x \neq 3 \\ \frac{9}{2} & \text { if } x=3\end{cases}$
Then $f$ is

• A

  continuous at all real numbers.
• Correct answer
  B

  continuous at all points in the domain.
• C

  discontinuous at only $x=-3$.
• D

  discontinuous at only $x=3$.

Hence, the correct answer is option: 'B'.