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The domain of \sin ^{-1}\left [ \log _{3}\left ( \frac{x}{3} \right ) \right ] is

  • Option 1)

    \left [ 1,9 \right ]

  • Option 2)

    \left [ -1,9 \right ]

  • Option 3)

    \left [ -9,1 \right ]

  • Option 4)

    \left [ -9,-1 \right ]

 

Answers (1)

As we learnt in 

Domains and Ranges of Inverse Trigonometric Functions -

For \sin ^{-1}x

Domain \epsilon \left [ -1, 1 \right ]

Range \epsilon \left [ -\frac{\pi }{2}, \frac{\pi }{2} \right ]

-

 

 For expression to be defined,

-1\leq log_{3} \: \frac{x}{3} \: \: \: \: \: \: \leq \: \: \: 1

\Rightarrow \frac{1}{3} \: \: \: \leq \frac{x}{3} \: \: \: 3

\Rightarrow 1 \: \: \: \leq x \: \: \: \leq \: \: \: 9

 

 


Option 1)

\left [ 1,9 \right ]

This option is correct

Option 2)

\left [ -1,9 \right ]

This option is incorrect

Option 3)

\left [ -9,1 \right ]

This option is incorrect

Option 4)

\left [ -9,-1 \right ]

This option is incorrect

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Vakul

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