Question 81
Let $f: \mathbb{Z} \to \mathbb{Z}$ be a function such that, for all integers $x$ and $y$, the following holds:
$$
f(f(x) - y) = f(y) - f(f(x)).
$$
Show that $f$ is bounded, ie. that there is a $C$ such that
$$
-C \lt f(x) \lt C
$$
for all $x$.
$$
f(f(x) - y) = f(y) - f(f(x)).
$$
Show that $f$ is bounded, ie. that there is a $C$ such that
$$
-C \lt f(x) \lt C
$$
for all $x$.