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

Explanation

`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.