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  4. Let K be the set of all real values of x where the function f(x) = sin |x| - |x| + 2(x - π ) cos |x| is not differentiable. Then the set K is equal to :

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Q. Let $K$ be the set of all real values of $x$ where the function $f(x) = \sin |x| - |x| + 2(x - \pi ) \cos |x|$ is not differentiable. Then the set $K$ is equal to :

JEE MainJEE Main 2019Continuity and Differentiability

Solution:

$f(x) = \sin|x|-|x| + 2(x - \pi) \cos x$
$\because \; \sin | x | - |x|$ is differentiable function at $x = 0$
$\therefore \; k = \phi $