If the function f(x)= cases -2 x & , if x - 2 A x+B & , if - 2 x 2 x & , if x 2 cases is continuous everywhere, then the values of A and B are respectively

Step-by-step solution

Since f (x) is continuous everywhere. f (x) is continuous at x=- 2 and x= 2 . aligned & _ x - ⁻ 2 f (x)= _ x - ⁺ 2 f (x) & _ x - 2 (-2 x)= _ x - 2 ( ~A x+ B ) & -2(-1)= A (-1)+ B & - A + B =2...(i) aligned aligned & Also, _ x ⁻ 2 f (x)= _ x ⁺ 2 f (x) & _ x 2 ( ~A x+ B )= _ x 2 ( x) & A (1)+ B =0 ...(ii) & ~A + B =0 aligned From (i) and (ii), we get A =-1, ~B =1