Let  fx=sgncot-1x+tanπ2x,  where [x] is the where [x] is the greatest integer function less than or equal to x. Then which of the following alternatives is/are true?

fx=sgncot-1x+tanπ2xsgncot-1x  is  defined  when  cot-1x  is  defined,  which  is  ∀x∈R.tanπ2x  is  defined  whenπ2x≠2n+12π,   Where n∈Z,or    x≠2n+1   or   x∉2n+1,2n+2.Hence,  domain  of  fx  is  ∪n∈Z2n+1,2n+2Also,  cot-1x>0∀x∈R.   Then           fx=1+tanπ2x=1∴         fx=1,x∈DfFrom the graph, f(x) is periodic with period 2.