The domain of f(x) = 1 _ 4 ( ^ - 1 x) - 1 ,is - Vidyadip

MCQ

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
$\left[ {0,\frac{1}{{\sqrt 2 }}} \right)$
✓
$\left( {0,\frac{1}{{\sqrt 2 }}} \right)$
D
$\left( { - \frac{1}{{\sqrt 2 }},\frac{1}{{\sqrt 2 }}} \right)$

✓

Answer

Correct option: C.

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

c
$\sin ^{-1} x>0$ .......$(1)$

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

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

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

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