The function `f(x)=e^(-|x|)` is continuous everywhere but not differentiable at `x=0` continuous and differentiable everywhere not continuous at `x=0` none of these

Explanation

We have given

`f(x)=e^(-|x|)`

Then

` f(x)=e^{-x}, x geq 0 `and

`e^{x}, x<0 `

LHL `=lim _{x ->0^-} f(x)=lim _{x->0} e^{x}=1`

RHL `=lim _{x ->0^{+}} f(x)=lim _{x -> 0} e^{-x}=1 `

Also, ` f(0)=e^{0}=1 `

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