A function is defined as follows :
`f(x)={{:(-(x)/(sqrtx^(2))",",xne0),(0",",x=0):}`
Which one of following is correct in respect of the above function?

Options

A. f(x) is continuous at x=0 but not differentiable at x=0
B. f(x) is continuous as well as differentiable at x=0
C. f(x) is discontinuous at x=0
D. None of the above

Answer

C

Explanation

`f(x)={{:((-x)/(sqrtx^(2))",",xne0),(0",",x=0):}`
`={{:((-x)/(|x|)",",xne0),(0",",x=0):}`
`f(0+h)=(-h)/(h)=-1,f(0-h)=(h)/(h)=1`
So, f(x) is discontinuous at x=0.