Let $f :\left[-\frac{1}{2}, 2\right]\to \mathbb{R}$ and $g:\left[-\frac{1}{2},2\right]\to \mathbb{R}$ be functions defined by $f\left(x\right)=\left[x^2-3\right]$ and $g\left(x\right)=\left|x\right|f\left(x\right)+\left|4x-7\right|f\left(x\right)$ , where $\left[y\right]$ denotes the greatest integer less than or equal to $y$ for $y\in \mathbb{R}$ . Then

• A

  $f$ is discontinuous exactly at three points in $\left[-\frac{1}{2},2\right]$
   
• Correct answer
  B

  $f$ is discontinuous exactly at four points in $\left[-\frac{1}{2},2\right]$
   
• Correct answer
  C

  $g$ is NOT differentiable exactly at four points in $\left(-\frac{1}{2}, 2\right)$
• D

  $g$ is NOT differentiable exactly at five points in $\left(-\frac{1}{2}, 2\right)$

Hence, the correct answer is options: 'B', 'C'.