# Function Discontinuity

Calculus Level 3

Consider the function

$\large{f\left( x \right) ={ \cot ^{ -1 }{ \left( \text{sgn}\left( \frac { \left\lfloor x \right\rfloor }{ 2x-\left\lfloor x \right\rfloor } \right) \right) } }}$

$$\text{Statement 1}$$: $$f(x)$$ is discontinuous at $$x=1$$.

$$\text{Statement 2}$$: $$f(x)$$ is non-differentiable at $$x=1$$.

Which of the following option is correct?

Notations: $$\text{sgn}$$ is signum function. And $$\left\lfloor . \right\rfloor$$ is floor function.

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