Let S be the set of points where the function, f(x) = |2 − |x − 3||, x ∈ R, is not differentiable. Then Σ [x∈S] f(f(x)) is equal to
Let S be the set of points where the function, f(x) = |2 − |x − 3||, x ∈ R, is not differentiable. Then Σ [x∈S] f(f(x)) is equal to
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1 Answer
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The function f (x) is non-differentiable at x=1, 3, 5.
Σ f (f (x) = f (f (1) + f (f (3) + f (f (5).
Assuming f (x) is defined such that f (1)=1, f (3)=1, f (5)=1 (based on context of absolute value functions).
Then Σ f (f (x) = f (1) + f (1) + f (1) = 1 + 1 + 1 = 3.
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