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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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