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  3. Mathematics
  4. The domain of the function f ( x )=√ log 2((1/ log 2 x )) is given by

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Q. The domain of the function $f ( x )=\sqrt{\log _2\left(\frac{1}{\log _2 x }\right)}$ is given by

Relations and Functions - Part 2

Solution:

$\log _2\left(\frac{1}{\log _2 x}\right) \geq 0$ ]
$\frac{1}{\log _2 x} \geq 1 ; \text { also } \log _2 x>0, x>1 $
$\log _x 2 \geq 1$
$2 \geq x \Rightarrow x \leq 2 $
$\therefore 1< x \leq 2 \Rightarrow \text { (3) }$