Let $S$ be the set of points where the function, $f(x)=|2-| x-3||, x \in R$, is not differentiable.

Question

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

Professor PC Thomas Classes · Answer

(3) : Since $f(x)$ is not differentiable at $x=1,3,5$.\So, $S=\{1,3,5\}$\ $	herefore \quad \sum_{x \in S} f(f(x))$\ $=f(f(1))+f(f(3))+f(f(5))$\ $=f(0)+f(2)+f(0)[\because f(1)=f(5)=0, f(3)=2]$\ $=1+1+1$\ $[\because f(0)=f(2)=1]$\ $=3$\