If f x = x + a , x ≤ 0 x - 4 , x > 0 and g x = x + 1 , x < 0 x - 4 2 + b , x ≥ 0 are continuous on R , then g o f 2 + f o g - 2 is equal to:

Step-by-step solution

Given f x = x + a ; x ≤ 0 x - 4 ; x > 0 and g x = x + 1 ; x < 0 x - 4 2 + b ; x ≥ 0 Given f x   &   g x are continuous on R So, for continuity f 0 - = f 0 = f 0 + ⇒ a = 0 - 4 ⇒ a = 4 And g 0 - = g 0 = g 0 + ⇒ 1 = 0 - 4 2 + b ⇒ b = 1 - 16 = - 15 Then, g f 2 + f g - 2 = g 2 + f - 1 = 2 - 4 2 - 15 + - 1 + 4 = 4 - 15 + 3 = - 8