Let f(x)=sgn(cot^(-1)x)+tan(pi/2[x]), wh...

Let `f(x)=sgn(cot^(-1)x)+tan(pi/2[x]),` where `[x]` is the greatest integer function less than or equal to `x ,` then which of the following alternatives is/are true? `f(x)` is many-one but not an even function. `f(x)` is a periodic function. `f(x)` is a bounded function. The graph of `f(x)` remains above the x-axis.

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