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23. Let \( f ( x ) = \operatorname { sgn } \left( \cot ^ { - 1 } x \right) + \tan \left( \frac { \pi } { 2 } [ x ] \right) , \) where \( \lfloor x | \) is the greatest integer function less than or equal to \( x \) . Then which of the following afternatives is/are true? \( f ( x ) \) is many-one but not an even function b. \( f ( x ) \) is a periodic function (. Fx) is a bounded function. d. The graph of \( f ( x ) \) remains above the \( x \) -axis.

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