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(C) The function is defined as $f(x) = \min\{-|x|, -\sqrt{1 - x^2}\}$.To find the points of non-differentiability,we look for the intersection points

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three elements

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(C) The function is defined as $f(x) = \min\{-|x|, -\sqrt{1 - x^2}\}$.To find the points of non-differentiability,we look for the intersection points of the curves $y = -|x|$ and $y = -\sqrt{1 - x^2}$.Setting $-|x| = -\sqrt{1 - x^2}$,we get $|x| = \sqrt{1 - x^2}$.Squaring both sides,$x^2 = 1 - x^2$,which implies $2x^2 = 1$,so $x^2 = \frac{1}{2}$,giving $x = \pm \frac{1}{\sqrt{2}}$.At $x = 0$,the function $f(x) = \min\{0, -1\} = -1$,which is a sharp corner for the function $-|x|$ and the intersection of the two curves.Checking the graph,the function $f(x)$ is non-differentiable at $x = -\frac{1}{\sqrt{2}}$,$x = 0$,and $x = \frac{1}{\sqrt{2}}$.Thus,there are $3$ points where the function is not differentiable. Therefore,$K$ has exactly three elements.

Let $f : (-1, 1) \to \mathbb{R}$ be a function defined by $f(x) = \min\{-|x|, -\sqrt{1 - x^2}\}$. If $K$ is the set of all points at which $f$ is not differentiable,then $K$ has exactly

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