The function given by y = ||x| - 1| is differ | vedclass

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(A) The function $f(x) = ||x| - 1|$ is non-differentiable at points where the expression inside the modulus becomes zero,as these points create sharp

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

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(A) The function $f(x) = ||x| - 1|$ is non-differentiable at points where the expression inside the modulus becomes zero,as these points create sharp corners in the graph.$1$. The inner modulus $|x|$ is non-differentiable at $x = 0$.$2$. The outer modulus $| |x| - 1 |$ is non-differentiable when $|x| - 1 = 0$,which implies $|x| = 1$,so $x = 1$ or $x = -1$.Thus,the function is non-differentiable at $x = \{-1, 0, 1\}$.Alternative method:Looking at the graph of $y = ||x| - 1|$,we can observe sharp turns (cusps) at $x = -1$,$x = 0$,and $x = 1$. $A$ function is not differentiable at points where its graph has sharp turns. Therefore,the function is not differentiable at $\{-1, 0, 1\}$.

The function given by $y = ||x| - 1|$ is differentiable for all real numbers except the points

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