jee-main 2024 Q73

jee-main · India · session2_04apr_shift2 Composite & Inverse Functions Find or Apply an Inverse Function Formula
If the function $f ( x ) = \left\{ \begin{array} { l l } \frac { 72 ^ { x } - 9 ^ { x } - 8 ^ { x } + 1 } { \sqrt { 2 } - \sqrt { 1 + \cos x } } , & x \neq 0 \\ a \log _ { e } 2 \log _ { e } 3 & , x = 0 \end{array} \right.$ is continuous at $x = 0$, then the value of $a ^ { 2 }$ is equal to
(1) 968
(2) 1152
(3) 746
(4) 1250
If the function $f ( x ) = \left\{ \begin{array} { l l } \frac { 72 ^ { x } - 9 ^ { x } - 8 ^ { x } + 1 } { \sqrt { 2 } - \sqrt { 1 + \cos x } } , & x \neq 0 \\ a \log _ { e } 2 \log _ { e } 3 & , x = 0 \end{array} \right.$ is continuous at $x = 0$, then the value of $a ^ { 2 }$ is equal to\\
(1) 968\\
(2) 1152\\
(3) 746\\
(4) 1250