Let $$f\left( x \right) = 15 - \left| {x - 10} \right|\,;\,x\,R.$$      Then the set of all values of $$x,$$ at which the function, $$g\left( x \right) = f\left( {f\left( x \right)} \right)$$     is not differentiable, is:

Solution :
$$\eqalign{ & {\text{Since, }}f\left( x \right) = 15 - \left| {\left( {10 - x} \right)} \right| \cr & \therefore g\left( x \right) = f\left( {f\left( x \right)} \right) = 15 - \left| {10 - \left[ {15 - \left| {10 - x} \right|} \right]} \right| \cr & = 15 - \left| {\left| {10 - x} \right| - 5} \right| \cr} $$
$$\therefore $$ Then, the points where function $$g\left( x \right)$$  is
Non-differentiable are
$$\eqalign{ & 10 - x = 0\,\,{\text{and }}\left| {10 - x} \right| = 5 \cr & \Rightarrow x = 10\,\,{\text{and }}x - 10 = \pm 5 \cr & \Rightarrow x = 10\,\,{\text{and }}x = 15,\,5 \cr} $$