Test Academy | Let f ( x ) = { 2 sin ⁡ ( x − 3 ) x − [ x ] ; x < 3 a | − x 2 − 12 + 7 | b ( x 2 + 12 x − 7 ) ; x > 3 b ; x = 3 is continuous at x = 3, then (a, b) is (2, 3), (1, 2), (2sin2, 3), None of these

Question

Let $f (x) = {\begin{cases} 2^{\frac{\sin (x - 3)}{x - [x]}} & ; & x < 3 \\ \frac{a | - x^{2} - 12 + 7 |}{b (x^{2} + 12 x - 7)} & ; & x > 3 \\ b & ; & x = 3 \end{cases}$ is continuous at x = 3, then (a, b) is

Options :

(2, 3)
(1, 2)
(2^sin2, 3)
None of these

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