Let f(x)=15-|x-10| ; x in R. Then,the set of | vedclass

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(D) Given $f(x) = 15 - |x - 10|$.We need to find the points where $g(x) = f(f(x))$ is not differentiable.First,$f(x)$ is not differentiable at $x = 10

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$\{5,10,15\}$

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(D) Given $f(x) = 15 - |x - 10|$.We need to find the points where $g(x) = f(f(x))$ is not differentiable.First,$f(x)$ is not differentiable at $x = 10$.Now,$g(x) = f(f(x)) = 15 - |f(x) - 10| = 15 - |(15 - |x - 10|) - 10| = 15 - |5 - |x - 10||$.The function $g(x)$ is not differentiable where the inner expressions are zero or where the original function $f(x)$ is not differentiable.$1$. $f(x)$ is not differentiable at $x = 10$.$2$. The expression inside the outer modulus,$5 - |x - 10|$,is zero when $|x - 10| = 5$,which gives $x - 10 = 5$ or $x - 10 = -5$,so $x = 15$ or $x = 5$.Thus,the function $g(x)$ 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 not differentiable,is

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