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If f(x)={:{(xe^(-(1/(|x|) + 1/x)), x ne ...

If `f(x)={:{(xe^(-(1/(|x|) + 1/x)), x ne 0),(0 , x =0 ):}` then f(x) is

A

discontinuous everywhere

B

continuous as well as differentiabe for all x

C

continuous for all x but not differentiable at x = 0

D

neither differentiable nor continuous at x = 0

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Verified by Experts

The correct Answer is:
C
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