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

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Aicharya · Accepted Answer

$\begin{aligned} & f(x)=15-|x-10| \ & \Rightarrow f(f(x))=f(15-|x-10|) \ & =15-|15-| x-10|-10| \ & =15-|5-| x-10||\end{aligned}$ graph has 3 corner points $x=5, x=10$ and $x=15$ So, it is not differentiable at $x \in\{5,10,15\}$

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…

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