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$The function f (x) = \frac{\sec^{- 1} x}{\sqrt{x - [x]}}, where [\cdot] denotes the greatest$ $integer less than or equal to x is defined for all x belonging to$

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R−{(−1,1)∪(n∣n∈Z)}

R+−(0,1)

R+−{n∣n∈N}

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detailed solution

Correct option is B

The function sec-1 x is defined for all x∈R --1,1 and the function 1x-x is defined for all x∈R -Z we know that x⩾ x and x =x for x∈Ztherefore domain of the given function =R --1,1∪n/n∈Z

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The function f(x)=sec−1⁡xx−[x], where [⋅] denotes the greatest integer less than or equal to x is defined for all x belonging to

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$The function f (x) = \frac{\sec^{- 1} x}{\sqrt{x - [x]}}, where [\cdot] denotes the greatest$ $integer less than or equal to x is defined for all x belonging to$