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Consider the function. f(x)={((a(7x-12-x...

Consider the function.
`f(x)={((a(7x-12-x^(2)))/(babs(x^(2)-7x+12)),x lt 3),(2^((sin(x-3))/(x-[x])),x gt 3),(b,x=3):}`
where `[x]` denotes the greatest integer less than or equal to `x` .If `"S"` denotes the set of all ordered pairs `(a,b)` such that `f(x)` is continuous at `x=3` ,then the number of elements in `S` is

A

4

B

2

C

1

D

Infiinitely many

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