# Let f

Question:

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

1. (1) five elements

2. (2) one element

3. (3) three elements

4. (4) two elements

Correct Option: , 3

Solution:

Consider the function

$f(x)=\max \left\{-|x|,-\sqrt{1-x^{2}}\right\}$

Now, the graph of the function

From the graph, it is clear that $f(x)$ is not differentiable at $x=0,-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}$

Then, $K=\left\{-\frac{1}{\sqrt{2}}, 0, \frac{1}{\sqrt{2}}\right\}$

Hence, $K$ has exactly three elements.

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