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(A) The function is given by $f(x) = ||x| - 1|$.We know that $|x|$ is not differentiable at $x = 0$.Also, the function $g(x) = |x| - 1$ is not differe

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$R - \{-1, 0, 1\}$

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(A) The function is given by $f(x) = ||x| - 1|$.We know that $|x|$ is not differentiable at $x = 0$.Also, the function $g(x) = |x| - 1$ is not differentiable at $x = 0$.The function $f(x) = |g(x)|$ is not differentiable where $g(x) = 0$ or where $g(x)$ is not differentiable.Setting $g(x) = 0$, we get $|x| - 1 = 0$, which implies $|x| = 1$, so $x = 1$ or $x = -1$.Additionally, $g(x)$ is not differentiable at $x = 0$.Therefore, $f(x)$ is not differentiable at $x \in \{-1, 0, 1\}$.Thus, the set of all values of $x$ for which $f(x)$ is differentiable is $R - \{-1, 0, 1\}$.

The set of all values of $x$ for which $f(x) = ||x| - 1|$ is differentiable is

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