Let f(x)=15-|x-10| ; x in R.


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

  1. (1) $\{5,10,15\}$

  2. (2) $\{10,15\}$

  3. (3) $\{5,10,15,20\}$

  4. (4) $\{10\}$

Correct Option: 1


Since, $f(x)=15-|(10-x)|$

$\therefore \mathrm{g}(\mathrm{x})=\mathrm{f}(\mathrm{f}(\mathrm{x}))=15-|10-[15-|10-\mathrm{x}|]|$

$=15-|| 10-x|-5|$

$\therefore$ Then, the points where function $g(x)$ is Nondifferentiable are

$10-x=0$ and $|10-x|=5$

$\Rightarrow x=10$ and $x-10=\pm 5$

$\Rightarrow x=10$ and $x=15,5$


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