Consider the function $\mathrm { f } ( \mathrm { x } ) = \left\{ \begin{array} { c l } \frac { \mathrm { a } \left( 7 \mathrm { x } - 12 - \mathrm { x } ^ { 2 } \right) } { \mathrm { b } \left| \mathrm { x } ^ { 2 } - 7 \mathrm { x } + 12 \right| } & , \mathrm { x } < 3 \\ 2 ^ { \frac { \sin ( \mathrm { x } - 3 ) } { \mathrm { x } - [ \mathrm { x } ] } } & , \mathrm { x } > 3 \\ \mathrm {~b} & , \mathrm { x } = 3 \end{array} \right.$, where $[ \mathrm { x } ]$ denotes the greatest integer less than or equal to x. If S denotes the set of all ordered pairs $( \mathrm { a } , \mathrm { b } )$ such that $\mathrm { f } ( \mathrm { x } )$ is continuous at $x = 3$, then the number of elements in S is: (1) 2 (2) Infinitely many (3) 4 (4) 1
Consider the function $\mathrm { f } ( \mathrm { x } ) = \left\{ \begin{array} { c l } \frac { \mathrm { a } \left( 7 \mathrm { x } - 12 - \mathrm { x } ^ { 2 } \right) } { \mathrm { b } \left| \mathrm { x } ^ { 2 } - 7 \mathrm { x } + 12 \right| } & , \mathrm { x } < 3 \\ 2 ^ { \frac { \sin ( \mathrm { x } - 3 ) } { \mathrm { x } - [ \mathrm { x } ] } } & , \mathrm { x } > 3 \\ \mathrm {~b} & , \mathrm { x } = 3 \end{array} \right.$, where $[ \mathrm { x } ]$ denotes the greatest integer less than or equal to x. If S denotes the set of all ordered pairs $( \mathrm { a } , \mathrm { b } )$ such that $\mathrm { f } ( \mathrm { x } )$ is continuous at $x = 3$, then the number of elements in S is:\\
(1) 2\\
(2) Infinitely many\\
(3) 4\\
(4) 1