A function is defined as follows:\({\rm{f}}\left( {\rm{x}} \right):\left\{ {\begin{array}{*{20}{c}} { - \frac{{\rm{x}}}{{\sqrt {{{\rm{x}}^2}} }},{\rm{\;x}} \ne 0}\\ {0.{\rm{\;x}} = 0} \end{array}} \right.\)Which one of the following is correct in respect of the above function?

f(x) is continuous at x = 0 but not differentiable at x = 0

f(x) is continuous as well as differentiable at x = 0

A function is defined as follows:\({\rm{f}}\left( {\rm{x}} \right):\le

1.	A function is defined as follows:\({\rm{f}}\left( {\rm{x}} \right):\left\{ {\begin{array}{*{20}{c}} { - \frac{{\rm{x}}}{{\sqrt {{{\rm{x}}^2}} }},{\rm{\;x}} \ne 0}\\ {0.{\rm{\;x}} = 0} \end{array}} \right.\)Which one of the following is correct in respect of the above function?
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» D. None of the above

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A function is defined as follows:\({\rm{f}}\left( {\rm{x}} \right):\left\{ {\begin{array}{*{20}{c}} { - \frac{{\rm{x}}}{{\sqrt {{{\rm{x}}^2}} }},{\rm{\;x}} \ne 0}\\ {0.{\rm{\;x}} = 0} \end{array}} \right.\)Which one of the following is correct in respect of the above function?

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