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If f(x)=|(log)e|x| , then f(x) is contin...

If `f(x)=|(log)_e|x|` , then `f(x)` is continuous and differentiable for all `x` in its domain] (b) `f(x)` is continuous for all `x` in its domain but not differentiable at `x=+-1` (c) `f(x)` is neither continuous nor differentiable at `x=+-1` (d) none of these

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`f(x)=|log_e|x||`
Clearly the funtion its not defined only at 0 and elsewhere it is defined,so it continuous everywhere in its domain.
We have to check its differentiability at `x=pm1`
`{df(x)}/{dx}=0` at `x=pm1`
`implies` it is not differentiable at `x=pm1`
Hence, option (b) is correct.
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