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:
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Official solution
g(x)=15−∣10−[15−∣10−x∣]∣=15−∣∣10−x∣−5∣. This is non-differentiable where 10−x=0 (i.e. x=10) and where ∣10−x∣=5 (i.e. x=10±5=5,15). So the set is {5,10,15}.