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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Continuity and Differentiability

NTA Abhyas 2020 · Mathematics · Continuity and Differentiability

Let f(x) = 10 - |x - 5|, x ∈ ℝ , then the set of all values of x at...

Let f(x)=10−∣x−5∣,x∈Rf\left(x\right) = 10 - \left|x - 5\right|, x \in \mathbb{R}, then the set of all values of xx at which f\l\left(f \left(x\right)\right) is not differentiable is

Options

  1. A{0,5,10}\left\{0,5, 10\right\}
  2. B{5,10}\left\{5,10\right\}
  3. C{0,5,10,15}\left\{0,5, 10,15\right\}
  4. D{5,10,15}\left\{5,10,15\right\}

Correct answer

A. {0,5,10}\left\{0,5, 10\right\}

Step-by-step solution

f(f(x))=10−f\left(f\left(x\right)\right) = 10 -\left|f\left(x\right) - 5\right| = 10 - \left|10 - \left|x - 5\right| - 5\right|<br/><br />= 10 - \left|5 - \left|x - 5\right|\right| ⇒ 10 - \left|\left|x - 5\right| - 5\right|
Points where f\lleft(f\left(x\right))isnon−differentiableare<br/>is non-differentiable are<br />x - 5 = 0 \left|x - 5\right| =5<br/><br />x = 5 x = 0, 10
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