Consider the function $f(x)=\left\{\begin{aligned} x^2-5, & x \leq 3 \\ \sqrt{x+13}, & x \gt 3\end{aligned}\right.$ Consider the following statements: 1. The function is discontinuous at $x=3$. 2. The function is not differentiable at $x=0$. Which of the above statements is/are correct?

• A

  1 only
• B

  2 only
• C

  Both 1 and 2
• Correct answer
  D

  Neither 1 nor 2

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