jee-main 2022 Q72

jee-main · India · session1_24jun_shift1 Composite & Inverse Functions Determine Domain or Range of a Composite Function
The domain of $f ( x ) = \frac { \cos ^ { - 1 } \left( \frac { x ^ { 2 } - 5 x + 6 } { x ^ { 2 } - 9 } \right) } { \log \left( x ^ { 2 } - 3 x + 2 \right) }$ is
(1) $x \in \left[ \frac { - 1 } { 2 } , 1 \right) \cup ( 2 , \infty ) - \{ 3 \}$
(2) $x \in \left[ \frac { - 1 } { 2 } , 1 \right] \cup ( 2 , \infty ) - \{ 3 \}$
(3) $x \in \left( \frac { - 1 } { 2 } , 1 \right) \cup [ 2 , \infty ) - \{ 3 \}$
(4) $x \in \left[ \frac { - 1 } { 2 } , 1 \right) \cup [ 2 , \infty ) - \{ 3 \}$
The domain of $f ( x ) = \frac { \cos ^ { - 1 } \left( \frac { x ^ { 2 } - 5 x + 6 } { x ^ { 2 } - 9 } \right) } { \log \left( x ^ { 2 } - 3 x + 2 \right) }$ is\\
(1) $x \in \left[ \frac { - 1 } { 2 } , 1 \right) \cup ( 2 , \infty ) - \{ 3 \}$\\
(2) $x \in \left[ \frac { - 1 } { 2 } , 1 \right] \cup ( 2 , \infty ) - \{ 3 \}$\\
(3) $x \in \left( \frac { - 1 } { 2 } , 1 \right) \cup [ 2 , \infty ) - \{ 3 \}$\\
(4) $x \in \left[ \frac { - 1 } { 2 } , 1 \right) \cup [ 2 , \infty ) - \{ 3 \}$