Question:
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:
Correct Option: 1
Solution:
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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