Let S be the set of points where the function , f(x) = | 2 - | x - 3 | , x ∈ R, is not differentiable. Then ∑ _ x ∈ S f(f(x)) is equal to

Correct answer: 0 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

JEE Main 20207 JanuaryMorning Shift

Exam: JEE Main
Year: 2020
Date: 7 January
Shift: Morning Shift
Subject: Mathematics
Chapter: Continuity and Differentiability

JEE Main 2020 · 7 January · Morning Shift · Mathematics · Continuity and Differentiability

Let S be the set of points where the function , f(x) = | 2 - | x -...

Let

S

be the set of points where the function

, f\left(x\right) = | 2 - | x - 3 | , x \in R,

is not differentiable. Then

\mathop{∑}_{x \in S}f\left(f\left(x\right)\right)

is equal to

Correct answer

Step-by-step solution

Check non-differentiability of function, we get,

$∵ f$ \left(x\right) $is non differentiable at$ x = 1, 3, 5 $<br />$ ∑ f\left(f\left(x\right)\right) = f\left(f\left(1\right)\right) + f\left(f\left(3\right)\right) + f\left(f\left(5\right)\right) $<br />$ = 1 + 1 + 1 $<br />$ = 3

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