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Let g(x) = f(x) + f(2+x), where  \( f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {1 - \left| x \right|,\;\;\left| x \right| \le 1}\\ {0,\;\;\left| x \right| > 1} \end{array}} \right.\) The number of points where the function g is not differentiable is

Let g(x) = f(x) + f(2+x), where  \( f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {1 - \left| x \right|,\;\;\left| x \right| \le 1}\\ {0,\;\;\left| x \right| > 1} \end{array}} \right.\) The number of points where the function g is not differentiable is Correct Answer 5

Concept :

}\\ {0, x > 1} \end{array}} \right.\). Thus the graph of f(x) would be as follows :

⇒ }\\ {0, x >1} \end{array}} \right.\)

⇒ The graph of g(x) would be as follows :

⇒ [ alt="F1 Ravi Sharma Anil 12-06.21 D18" src="//storage.googleapis.com/tb-img/production/21/06/F1_Ravi%20Sharma_Anil_12-06.21_D18.png" style="width: 453px; height: 217px;">

⇒ Thus, according to the concept explained, g(x) is not differentiable at 5 points.

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