Let f(x) = 15 - |x - 10|; x ∈ R. Then the set of all values of x, at which the function g(x) = f(f(x)) is not differentiable, is?

Correct option is C.
5, 10, 15
f(x) = 15 - |x - 10|, x ∈ R
f(f(x)) = 15 - |f(x) - 10| = 15 - |15 - |x - 10| - 10| = 15 - |5 - |x - 10||
x = 5, 10, 15 are points of non-differentiability
Aliter:
At x = 10, f(x) is not differentiable.
Also, when 15 - |x - 10| = 10 ⇒ x = 5, 15
∴ non-differentiability points are 5, 10, 15.