Let 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 If f ( x ) is continuous for 0 x , then

Step-by-step solution

_ x ⁻ 4 f(x)= _ x ⁻ 4 x+a 2 x _ x ⁺ 4 f(x)= _ x ⁺ 4 2 x x+b _ x ⁻ 2 f(x)= _ x ⁻ 2 2 x x+b aligned & _ x ⁺ 2 f(x)= _ x ⁺ 2 a 2 x-b x & =a 2 ( 2 )-b ( 2 ) aligned Since f(x) is continuous at 4 and 2 , we write 4 + a = 2 + b [ From (1) and (2) ] b =- a - b [ From (3) and (4) ]