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$\begin{array}{l} T h e s e t o f a l l v a l u e s o f x a n d t h e s e t o f a l l v a l u e s o f a f o r w h i c h t h e r e a l v a l u e d f u n c t i o n \\ f (x) = \sqrt{\log_{a} (x - [x])} i s d e f i n e d a r e r e s p e c t i v e l y \end{array}$

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a

$R - Z & (0, 1)$

b

$Z & R - {0, 1}$

c

$Z - & (1, \infty)$

d

$R & R$

answer is A.

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Detailed Solution

$\begin{array}{l} f (x) = \sqrt{\log_{a} (x - [x])} i s d e f i n e d i f f \\ \log_{a} (x - [x]) \geq 0, a n d a > 0 a n d a \neq 1 \\ \Rightarrow x - [x] \geq a^{0}, ∴ a \in (0, 1) \\ \Rightarrow x - [x] \geq 1 \\ n o t p o s s i b l e ∴ x - [x] > 0 \\ x \in R - [Z] \end{array}$

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