If `[.]` and `{.}` denote greatest and fractional part functions respectively and `f(x)={(x((e^([x]+|x|)-2)/([x]+{2x})),x!=0),(-1,x=0):}` then

Options

A. `f(x)` is differentiable every where
B. `f(x)` is continuous at `x=0`
C. `f(x)` is continuous every where
D. `f(x)` is not differentiable at `x=0`

Answer

D

Explanation

`lim_(xrarr0^(+))f(x)=lim_(xrarr0^(+))x((e^(x)-2)/(2x))=-1/2!=-1`
`:.f(x)` is not continuous at `x=0`
`:.f(x)` is not differentiable at `x=0`