If the function f (x) is continuous in 0 x , then the value of 2 a+3 b is where f(x)= cases x+a 2 x & if 0 x < 4 2 x x+b & if 4 x 2 a 2 x-b x & if 2 < x cases

Step-by-step solution

f (x) is continuous in 0 x f (x) is continuous at x= 4 . aligned & _ x ⁻ 4 f (x)= _ x ⁺ 4 f (x) & _ x 4 ⁻ (x+ a 2 x)= _ x ⁺ 4 (2 x x+ b ) & 4 + a 2 4 =2 4 4 + b & 4 + a = 2 + b & a - b = 4 ... (i) aligned Also, f (x) is continuous at x= 2 . aligned & _ x ⁻ 2 f (x)= _ x ⁺ 2 f (x) & _ x ⁻ 2 (2 x x+ b )= _ x ⁺ 2 ( a 2 x- b x) & 2 2 2 + b = a (2 2 )- b 2 & b =- a - b & a =-2 ~b aligned Substituting a=-2 b in equation (i), we get aligned & -2 b-b= 4 & b= - 12 & a=-2 - 12 = 6 aligned Now, aligned 2 a +3 ~b & =2 ( 6 )+3 (