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1.Relation and Function
normal
$f(x) = \frac{1}{{\sqrt {{{\log }_{\frac{\pi }{4}}}({{\sin }^{ - 1}}x) - 1} }}$ નો પ્રદેશગણ મેળવો.
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
