Consider the function. f(x)= {(a(7 x-12-x^2))/(b|x^2-7 x+12|), x<3; 2^((sin (x-3))/(x-[x])), x>3; b, x=3,} where [x] denotes the greatest integer…

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