The values of a and b , so that the function f (x)= cases x+ a 2 x & , 0 x 4 2 x x+ b & , 4 x 2 a 2 x- b x & , 2 x cases is continuous for 0 x , are respectively given by

Step-by-step solution

As the given function is continuous at x= 4 and 2 , we get _ x ⁻ 4 f (x)= _ x ⁺ 4 f (x) aligned & _ x 4 (x+a 2 x)= _ x 4 (2 x x+b) & 4 +a= 2 4 +b & a-b= 4 ...(i) aligned Also, _ x ⁻ 2 f (x)= _ x ⁺ 2 f (x) aligned & _ x 2 (2 x x+b)= _ x 2 (a 2 x-b x) & 0+b=-a-b & a+2 b=0...(ii) aligned Solving equations (i) and (ii), we get a= 6 and b= - 12