question_answer

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

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)  Both (b) and (c)

E)  None of these