JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1

The domain of the function

f\left( x \right) = {\sin ^{ - 1}}\left( {{{\log }_3}\left( {x/3} \right)} \right)

View answer and explanation

Correct option: A

\left[ {1,\;9} \right]

Option A ([1, 9]) is correct because the argument of the arcsine function must be between -1 and 1, leading to the inequality -1 <= log_3(x/3) <= 1, which simplifies to 1 <= x <= 9.

More Questions from FUNCTIONS

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f:(-\infty, 2] \longrightarrow(-\infty, 4]

, where

f(x)=x(4-x)

, then

f^{-1}(x)

is given by: If

g(f(x))=|\sin x|

and

f(g(x))=(\sin \sqrt{x})^2

, then Let

f:\left( {2,\;3} \right) \to \left( {0,\;1} \right)

be defined by

f\left( x \right) = x - \left[ x \right]

, then

{f^{ - 1}}\left( x \right)

equals Let

f: R \rightarrow R

be defined as

f(x)=x^4

, Choose the correct answer. Which of the following functions are odd functions Let

f(x)=(x+1)^2-1(x \geq-1)

. Then the set

S=\left\{x: f(x)=f^{-1}(x)\right\}

contains