Question

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The domain of ( f(x)=sin ^{-1}left{log _{3}left(frac{x^{2}}{3}right)right} ) is
1) ( (-infty, 3] )
2) ( [3, infty) )
3) [-3,-1]( cup[1,3] )
4) (-9,-1)( cup(1,9) )

JEE/Engineering Exams

Maths

Solution

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$The domain of f(x)=sin^−1{log_3(x^2/3)} is$

( f(x)=sin ^{-1}left{log _{3}left(frac{x^{2}}{3}right)right} )
2) ( -1 leq log _{3} frac{x^{2}}{3} leq 1 )
( Rightarrow frac{1}{3} leq frac{x^{2}}{3} leq 3 )
(Rightarrow) 1 leq x^{2} leq 9 )
(1) ( x in[-3,-1] cup[1,3] )

Options 3

The domain of ( f(x)=sin ^{-1}left{log _{3}left(frac{x^{2}}{3}right)right} ) is1) ( (-infty, 3] )2) ( [3, infty) )3) [-3,-1]( cup[1,3] )4) (-9,-1)( cup(1,9) )

The domain of ( f(x)=sin ^{-1}left{log _{3}left(frac{x^{2}}{3}right)right} ) is
1) ( (-infty, 3] )
2) ( [3, infty) )
3) [-3,-1]( cup[1,3] )
4) (-9,-1)( cup(1,9) )