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(C) The expression $x-[x]$ represents the fractional part of $x$,denoted as $\{x\}$.Since $x$ is a real number,the fractional part $\{x\}$ lies in the

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$(1, \infty)$

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(C) The expression $x-[x]$ represents the fractional part of $x$,denoted as $\{x\}$.Since $x$ is a real number,the fractional part $\{x\}$ lies in the interval $[0, 1)$.However,the denominator $\sqrt{x-[x]}$ cannot be zero,so $x-[x] 
eq 0$.Therefore,$x-[x] \in (0, 1)$.As $x-[x]$ approaches $0$ from the right,$\frac{1}{\sqrt{x-[x]}}$ approaches $\infty$.As $x-[x]$ approaches $1$ from the left,$\frac{1}{\sqrt{x-[x]}}$ approaches $1$.Thus,the range of $f(x)$ is $(1, \infty)$.

If $[x]$ denotes the greatest integer $\leq x$,then the range of the real-valued function $f(x) = \frac{1}{\sqrt{x-[x]}}$ is

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