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

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