let [x] is GIF, if F(x) = [ x sinpix ], then F(x) is

1  not continous at x = 0

2   not continous in ( -1,1)

3   not differentiable at x =1

4   differentiable in ( -1 , 1)

ok  firstly try drawing rough graph

lim x tend to 0..

RHL = [ h sinh ] = 0

LHL = [ -h sin( - h) ] = 0

so it is continuous at 0.

by inspection we see that it is continuous in (-1,1)

check at x = 1

LHL = [ (1 + h) sin(h + 1) ] = [-(1 + h) sinh] =-1

RHL = [(1 -h) sin(1 -h)]  =  [(1 - h) sinh ] = 0 

so it is discontinuos at x = 1

When f is discontinuous at x=1,it won't be differentiable at x=1.So,ans is option(3)