jee-main 2023 Q77

jee-main · India · session2_12apr_shift1 Composite & Inverse Functions Determine Domain or Range of a Composite Function

Let $D$ be the domain of the function $f ( x ) = \sin ^ { - 1 } \left( \log _ { 3 x } \left( \frac { 6 + 2 \log _ { 3 } x } { - 5 x } \right) \right)$. If the range of the function $g : D \rightarrow \mathbb { R }$ defined by $g ( x ) = x - [ x ]$, ([x] is the greatest integer function), is $( \alpha , \beta )$, then $\alpha ^ { 2 } + \frac { 5 } { \beta }$ is equal to
(1) 135
(2) 45
(3) 46
(4) 136

Let $D$ be the domain of the function $f ( x ) = \sin ^ { - 1 } \left( \log _ { 3 x } \left( \frac { 6 + 2 \log _ { 3 } x } { - 5 x } \right) \right)$. If the range of the function $g : D \rightarrow \mathbb { R }$ defined by $g ( x ) = x - [ x ]$, ([x] is the greatest integer function), is $( \alpha , \beta )$, then $\alpha ^ { 2 } + \frac { 5 } { \beta }$ is equal to\\
(1) 135\\
(2) 45\\
(3) 46\\
(4) 136

Paper Questions

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