Choose the correct answer.

The function f(x) = e^–|x| is

Given that f(x) = e^–|x|

Checking continuity and differentiability at x = 0,

LHL:

RHL:

And f(0)= 1

∵ LHL = RHL = f(0)

f(x) is continuous at x = 0.

LHD at x =0,

∵ LHD does not exist, so f(x) is not differentiable at x =0.

Hence, option A is correct.