Let S be the set of points where the functions $$fx=2$$−x−$$3$$,x∈R , is not differentiable. Then ∑x∈Sffxis equal to $$____$$.

$$fx=2$$−x−$$3F$$ is not differentiable at $$x=1$$,$$3$$,$$5$$ ⇒∑x∈$$sffx=ff1+ff3+ff5=f0+f2+f0=1+1+1=3$$

Differentiability

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Question

Let S be the set of points where the functions $f (x) = |2 - |x - 3||$ , $x \in R$ , is not differentiable. Then $\sum_{x \in S} f (f (x))$ is equal to ____.

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Solution

$f (x) = |2 - |x - 3||$
F is not differentiable at x=1,3,5
$\Rightarrow \sum_{x \in s} f (f (x)) = f (f (1)) + f (f (3)) + f (f (5))$ $= f (0) + f (2) + f (0)$ $= 1 + 1 + 1 = 3$

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