Solve this following


Let $f(\mathrm{x})=15-|\mathrm{x}-10| ; \mathrm{x} \in \mathrm{R}$. Then the set of all values of $\mathrm{x}$, at which the function, $\mathrm{g}(\mathrm{x})=f(f(\mathrm{x}))$ is not differentiable, is :

  1. $\{5,10,15,20\}$

  2. $\{10,15\}$

  3. $\{5,10,15\}$

  4. $\{10\}$

Correct Option: , 3


$f(\mathrm{x})=15-|\mathrm{x}-10|, \mathrm{x} \in \mathrm{R}$


$=15-|15-| \mathrm{x}-10|-10|$

$=15-|5-| \mathrm{x}-10||$

$x=5,10,15$ are points of non differentiability

Aliter :

At $\mathrm{x}=10 f(\mathrm{x})$ is non differentiable

also, when $15-|x-10|=10$

$\Rightarrow x=5,15$

$\therefore$ non differentiability points are $\{5,10,15\}$


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