Question: If f(x)= |ln|x|-1| find non differentiable points inits domain?

Hi Swati,

Concept for the problem: From the fraph of f(x), when you need to get the graph of f(|x|)

For f(|x|), you note for x = a and x = -a. the value of f(|x|) is the same.

So you are trying to make f(x) even by removing the those values of f(x) in the domain x<0, and then for x>0, you tke the reflection of f(x) about the y-axis.

So to get graph of ln|x|, (as lnx has domain x>0), you just take the reflection of lnx about the y-axis to get ln|x|.

Now ln|x| - 1 is easily obtained by shifting the graph 1 unit downwards,

Next, from the graph of f(x), we want graph of |f(x)|.

For this, you retain the graph where f(x) is greater than 0, and where f(x) < 0, you would take the reflection about the x-axis to make it positive (ie would be above x-axis)

All the best.

Regards,

Ashwin (IIT Madras)