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Let f:[-1/2,2] rarr R and g:[-1/2,2] rar...

Let `f:[-1/2,2] rarr R` and `g:[-1/2,2] rarr R` be 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 `yinR`. Then,

A

f is discontinuous exactly at three points in `[-1/2,2]`

B

f is discontinuous exactly at four points in `[-1/2,2]`

C

g is NOT differentiable exactly at four points in `(-1/2,2)`

D

g is NOT differentiable exactly at five points in `(-1/2,2)`

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The correct Answer is:
B, C
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