JEE MAIN - Mathematics (2020 - 7th January Morning Slot - No. 11)
Let S be the set of points where the function, ƒ(x) = |2-|x-3||, x $$ \in $$ R is not differentiable. Then $$\sum\limits_{x \in S} {f(f(x))} $$ is equal to_____.
Answer
3
Explanation
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f(x) is non-differentiable at x = 1, 3, 5
$$ \therefore $$ S is {1, 3, 5}
$$\sum\limits_{x \in S} {f(f(x))} $$
= f(f(1)) + f(f(3)) + f(f (5))
= f(0) + f(2) + f(0)
= 1 + 1 + 1 = 3
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