JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(S\) be the set of points where the function, \(f(\mathrm{x})=|2-| \mathrm{x}-3 \|, \mathrm{x} \in \mathrm{R},\) is not differentiable. Then \(\sum\limits_{\mathrm{x\in s}} f(f(\mathrm{x}))\) is equal to
- A \(5\)
- B \(2\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(C) \(3\)
Step-by-step Solution
Detailed explanation
\(f(x)=|2-| x-||3\) \(f\) is not differentiable at \(x=1,3,5\) \(\sum_{\mathrm{xes}} \mathrm{f}(\mathrm{f}(\mathrm{x}))=\) \( \mathrm{f}(\mathrm{f}(1))+\mathrm{f}(\mathrm{f}(3))+\mathrm{f}(\mathrm{f}(5)) \) \(=\mathrm{f}(0)+\mathrm{f}(2)+\mathrm{f}(0) \) \(=1+1+1=3 \)
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