let $f:\left[-\frac{1}{2}, 2\right] \rightarrow R$ and $g:\left[-\frac{1}{2}, 2\right] \rightarrow R$ be functions defined by $f(x)=\left[x^2-3\right]$ and $g(x)=|x| f(x) +|4 x-7| f(x)$, where $[y]$ denotes the greatest integer less than or equal to $y$ for $y \in R$. Then
Select ALL correct options:
A
$f$ is discontinuous exactly at three points in $\left[-\frac{1}{2}, 2\right]$
B
$f$ is discontinuous exactly at four points in $\left[-\frac{1}{2}, 2\right]$
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 $\left(-\frac{1}{2}, 2\right)$
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