Let $g: \mathbb{R} \longrightarrow \mathbb{R}$ be the function given by
$g(x)= \begin{cases}|x|^x & \text { if } x \neq 0 \\ 1 & \text { if } x=0\end{cases}$

Then

• A

  $g$ is differentiable at $x=0$
• B

  $g$ is a strictly increasing function on $\mathbb{R}$
• Correct answer
  C

  $g$ is continuous at $x=0$
• D

  $g(x)=0$ for some $x \in \mathbb{R}$

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