The document defines the function f(f(x)) and shows that it equals x+1. It then defines f(f(f(x))) and shows that it equals 3+2x. It concludes that for these functions to be defined, x cannot equal -1 or 2.

1. 1+ x
( )
f ( f ( x)) =
1
∗ 1 = 1+ x = x +1
1 1+ x 1+1+ x x + 2
(1 + ) ( )
1+ x 1
So x ≠ 2
−
1 1+x
(( ) +1) ( )
1+x 1 1 +1 + x 2 +x
f ( f ( f ( x ))) = ∗ = =
1 1+x 2 +1 +2 x 3 +2 x
(( ) +2) ( )
1+x 1
So −3
x≠
2
And from original problem, x ≠ −1