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The domain of the function f\left ( x \right )= \frac{\sin ^{-1}\left ( x-3 \right )}{\sqrt{9-x^{2}}} is

  • Option 1)

    \left [ 1,2 \right ]

  • Option 2)

    \left [ 2,3 \right \left \right )

  • Option 3)

    \left [ 2,3 \right ]

  • Option 4)

    \left [ 1,2 \right \left \right )

 

Answers (1)

best_answer

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 (x-3)\leq 1 \: \: and \: \: 9-x^{2}> 0

\Rightarrow 2\leq x\leq 4 \: \: and \: \: -3< x< 3

Combining, we get 2\leq x< 3


Option 1)

\left [ 1,2 \right ]

This option is incorrect

Option 2)

\left [ 2,3 \right \left \right )

This option is correct

Option 3)

\left [ 2,3 \right ]

This option is incorrect

Option 4)

\left [ 1,2 \right \left \right )

This option is incorrect

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