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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