Question

f(x) = |log_e |x||, then

A. f(x) is continuous and differentiable for all x in its domain

B. f(x) is continuous for all for all x in its domain but bot differentiable at x = ±1

C. f(x) is neither continuous nor differentiable at x = ±1

D. None of these

Answer 1

Correct answer is B.

Given that the f(x) = |log|x|| where

We can see that function is continuous for all x. Now, checking the points of non differentiability.

LHD at x = 1,

∵ LHD ≠ RHD

So, function is not differentiable at x =1.

LHD at x = -1,

∵ LHD ≠ RHD

So, function is not differentiable at x = -1.

At x = 0 function is not defined.

∴ Function is not differential at x = 0 and ±1.