QJEEM22Mafe7b: JEE Main 2022 Mathematics - Class 12 JEEM22Mafe7b Solution: The domain of the function , where [t] is the greatest integer…

- 1 \le 2{x^2} - 3 < 2

or 2 \le 2{x^2} < 5

or 1 \le {x^2} < {5 \over 2}

$x \in \left( { - \sqrt {{5 \over 2}} , - 1} \right] \cup \left[ {1,\sqrt {{5 \over 2}} } \right)$

{\log _{{1 \over 2}}}({x^2} - 5x + 5) > 0

0 < {x^2} - 5x + 5 < 1

{x^2} - 5x + 5 > 0 & {x^2} - 5x + 4 < 0

$x \in \left( { - \infty ,{{5 - \sqrt 5 } \over 2}} \right) \cup \left( {{{5 + \sqrt 5 } \over 2},\infty } \right)$

& $x \in ( - \infty ,1) \cup (4,\infty )$

Taking intersection

$x \in \left( {1,{{5 - \sqrt 5 } \over 2}} \right)$