=1+ 2 , - < x 1 If the function f ( x )= ax + b , 1 < x < 3 is continuous in =6 x 12 , 3 x < 6 (- , 6) , then the values of a and b are respectively.

Step-by-step solution

aligned & _ x 1⁻ f(x)= _ x 1⁻ 1+ 2 =1+1=2 & _ x 1⁺ f(x)= _ x 1⁺ a+b=a+b aligned Since f(x) is continuous at x=1 , we get a+b=2 [From (1), (2)] aligned & _ x 3⁻ f(x)= _ x 3⁻ a x+b=3 a+b & _ x 3⁺ f(x)= _ x 3⁺ 6 x 12 =6 3 12 =6 aligned Since f(x) is continuous at x=3 , we get 3 a+b=6 [From (4), (5)] Solving (3) and (6), we get a =2, b=0