The domain of $\frac{{cos}^{- 1} x}{[x]}$ where $[.]$ represent greatest integer function is given by

{| x | \leq 1} - {0 \leq x < 1}

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[- 1, 0) \cup {1}

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[- 1, 1]

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[- 1, 1] - {0}

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Solution

The correct options are
A ${| x | \leq 1} - {0 \leq x < 1}$
B $[- 1, 0) \cup {1}$
For given function to be defined,
$(i) D_{1} :$ for ${cos}^{- 1} x$ to be defined, $- 1 \leq x \leq 1$
$(i i) D_{2} :$ for $\frac{1}{[x]}$ to be defined, $[x] \neq 0 \Rightarrow x \in R - [0, 1)$
Hence required domain is $D_{1} \cap D_{2}$ which is $[- 1, 0] \cup {1}$

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