Let f x = x - 1 x + 1 , x ∈ R - 0 , - 1 , 1 ) . If f n + 1 x = f f n x for all n ∈ N , then f 6 6 + f 7 7 is equal to

Step-by-step solution

Given f x = x - 1 x + 1 = f 1 x ⇒ f 2 x = f f x = x - 1 x + 1 - 1 x - 1 x + 1 + 1 = - 1 x Now f 3 x = f f 2 x = f - 1 x = x + 1 1 - x ⇒ f 4 x = f x + 1 1 - x = - 1 x ⇒   f 6 x = - 1 x ⇒ f 6 6 = - 1 6 So f 7 x = - 1 x = x + 1 1 - x ⇒ f 7 7 = 8 - 6 = - 4 3 ∴ - 1 6 + - 4 3 = - 3 2