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Q.

The real valued function  f(x)=cosec−1xx−[x], where x denotes the greatest integer less than or equal to x, is defined for all x belongs to

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a

R-Z

b

all integers except 0,-1,1

c

R-Z ∪ [-1,1]

d

all reals except the interval [-1,1]

answer is C.

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Detailed Solution

f(x)=cosec-1(x)x-[x]cosec-1x is defined  for all |x|≥1 x≤-1 or x≥1x≠[x] ⇒x does not integral values∴x∉z and x∉[-1,1]
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