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$I f [x] d e n o t e s t h e g r e a t e s t int e g e r f u n c t i o n, t h e n t h e d o m a i n o f t h e f u n c t i o n f (x) = \sqrt{\frac{x - [x]}{\log (x^{2} - x)}} i s$

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$(1, \infty)$

$(1, \infty) - Z$

$R - [\frac{1 - \sqrt{5}}{2}, \frac{1 + \sqrt{5}}{2}]$

$[\frac{1 - \sqrt{5}}{2}, \frac{1 + \sqrt{5}}{2}]$

answer is C.

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Detailed Solution

$f (x) = \sqrt{\frac{x - [x]}{\log (x^{2} - x)}}$ is defined iff

$\frac{x - [x]}{\log (x^{2} - x)} \geq 0 \Rightarrow \log (x^{2} - x) >0 \Rightarrow x^{2} - x > 1 \Rightarrow x^{2} - x - 1 > 0 \Rightarrow x = \frac{1 \pm \sqrt{5}}{2} D o m a i n = R - [\frac{1 - \sqrt{5}}{2}, \frac{1 + \sqrt{5}}{2}]$

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