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Consider the function. 3 x , b 3 x , 2 3 x , | 12 x 7 – x | b ) x – 12 – x 7 ( a ] x [ – x ) 3 – x sin( 2 2 = > < + f(x) = Where [x] denotes greatest integer less than or equal to, 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 :

1. Infinitely many
2. 2
3. 1
4. 4

Correct answer: 1

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