The function f(x)= array l a |x^2-x-6 | 6+x-x^2 , x 3 b _ x 3 ( x ₃^x t d t x-3 ), x=3 x-[x] x-3 , x 3 array . is continuous at x=3 . If f(3) 0 , then a, b is (where [ ] denotes the greatest integer function)

Step-by-step solution

f(x) is continuous at x=3 f (3⁻ )= f (3)= f (3⁺ ) Now f (3⁻ )= _ x 3⁻ a |x^2-x-6 | 6+x-x^2 = _ x 3⁻ -a (x^2-x-6 ) 6+x-x^2 =a aligned & f (3⁺ )= _ x 3⁺ x-[x] x-3 = _ x 3⁺ x-3 x-3 =1 & f(3)=b _ x 3 ( x ₃^x t d t x-3 ) ( 0 0 form )=b _ x 3 ( x^2+ ₃^x t d t 1 )=9 b aligned a=9 b=1 b= 1 9 and a=1