Let $ S $ be the set of points where the function, $ f(x)=|2-| x-3 \mid, x \in R $, is not differentiable. Then $ \sum_{x \in S} f(f(x)) $ is equal to

Question

Let $ S $ be the set of points where the function, $ f(x)=|2-| x-3 \mid, x \in R $, is not differentiable. Then $ \sum_{x \in S} f(f(x)) $ is equal to,

MARKS App · Accepted Answer

Check non-differentiability of function, we get, ∵ f x is non differentiable at x = 1 , 3 , 5 ∑ f f x = f f 1 + f f 3 + f f 5 = 1 + 1 + 1 = 3

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