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Let f(x) = 15 - |x - 10| for x ∈ R. The function g(x) = f(f(x)) fails to be differentiable at which of the following sets of x-values?

1. {5, 10, 15}
2. {10, 15}
3. {5, 10, 15, 20}
4. {10}

Correct answer: {5, 10, 15}

Solution

g(x)=f(f(x)) with f(x)=15-|x-10|. Non-differentiability occurs at the inner kink x=10 and where f(x)=10, i.e. |x-10|=5 -> x=5,15. So the set is {5,10,15}.

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