A function is defined as follows Which one of the following is correct in respect of the above funct...........

Mathematics (NDA) Relations and Functions

A function is defined as follows:

$f(x)=\left\{\begin{matrix} -\frac{x}{\sqrt{x^{2}}} &,x\neq 0 \\ 0 & ,x=0 \end{matrix}\right.$

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

f(x) is discontinuous at x = 0

None of the above

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