The set of all values of x and the set of all | vedclass

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(A) For the function $f(x) = \sqrt{\log_a(x - [x])}$ to be defined, the expression inside the square root must be non-negative and the logarithm must

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$R - Z$ and $(0, 1)$

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(A) For the function $f(x) = \sqrt{\log_a(x - [x])}$ to be defined, the expression inside the square root must be non-negative and the logarithm must be defined.$1$. The term $(x - [x])$ represents the fractional part of $x$, denoted as $\{x\}$. Since $0 \leq \{x\}  0$, which implies $x 
otin Z$.$2$. For the square root to be defined, $\log_a(\{x\}) \geq 0$.$3$. If $a > 1$, then $\{x\} \geq a^0 = 1$. Since $\{x\} $4$. If $0 $5$. Thus, $x \in R - Z$ and $a \in (0, 1)$.

The set of all values of $x$ and the set of all values of $a$ for which the real-valued function $f(x) = \sqrt{\log_a(x - [x])}$ is defined are respectively:

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