Domain of f(x) = frac{1}{{√ {{{log }_{frac{π }{4}}}({{sin }^{ - 1}}x) - 1} }} ,is

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1.Relation and Function

normal

The domain of $f(x) = \frac{1}{{\sqrt {{{\log }_{\frac{\pi }{4}}}({{\sin }^{ - 1}}x) - 1} }}$,is

A

$\left( { - 1,\frac{1}{{\sqrt 2 }}} \right)$

B

$\left[ {0,\frac{1}{{\sqrt 2 }}} \right)$

C

$\left( {0,\frac{1}{{\sqrt 2 }}} \right)$

D

$\left( { - \frac{1}{{\sqrt 2 }},\frac{1}{{\sqrt 2 }}} \right)$

Solution

$\sin ^{-1} x>0$ …….$(1)$

$\log _{\frac{\pi}{4}}\left(\sin ^{-1} x\right)-1>0$

$ \Rightarrow \sin ^{-1} x<\frac{\pi}{4}$

from $( 1)$ $\cap(2) \Rightarrow \mathrm{x} \in\left(0, \frac{1}{\sqrt{2}}\right)$

Standard 12

Mathematics

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(JEE MAIN-2023)