Given $f (x) = | | x - 1 | - 1 |$ , then number of point of non differentiability of $f (x)$ is

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Solution

From the graph of function $f (x) = | x - 1 | - 1 | |$ , we can see that sharp corner is present at points $x = 0, 1, 2$ which implies $L H D$ and $R H D$ are finite but unequal. So, $f (x)$ is continuous but not differentiable at $3$ points.

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