If the function given by f(x)= cases -2 x & - x < -( / 2) a x+b & -( / 2) < x < ( / 2) x & ( / 2) x cases is continuous in [- , ] , then the value of (3 a+2 b)^3 is

Step-by-step solution

aligned & _ x ⁻ 2 f(x)= _ x ⁻ 2 -2 x=-2 (- 2 )=2 & _ x - ⁺ 2 f(x)= _ x - ⁺ 2 a x+b=a ( - 2 )+b=-a aligned Since f(x) is continuous at x= - 2 , we write aligned & 2=-a+b & _ x ⁻ 2 f(x) _ x ⁻ 2 a x+b=a ( 2 )+b=a+b & _ x ⁺ 2 f(x)= _ x ⁺ 2 x= ( 2 )=0 aligned Since f(x) is continuous at x= 2 , we write a + b =0 From (1) and (2), we get a =-1, ~b =1 (3 a+2 b)^3=(-3+2)^3=-1