Q.

Let f(x)=nx+n−nx+n+tanπx2, where [x] is the greatest integer ≤x and n∈N. It is

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a

a periodic function of period 1

b

a periodic function of period 4

c

not periodic

d

a periodic function of period 2

answer is D.

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Detailed Solution

nx+n−nx+n has the period 1/n and tanπx2 has the period ππ/2 i.e, LCM of 1/n, 2 is 2.
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Let f(x)=nx+n−nx+n+tanπx2, where [x] is the greatest integer ≤x and n∈N. It is