Question 98
Find all real numbers $a$ for which there exists a function $f$ defined on the set of all real numbers which takes as its values all real numbers exactly once and satisfies the equality
$$
f(f(x)) = x^2 f(x) + a x^2
$$
for all real $x$.
$$
f(f(x)) = x^2 f(x) + a x^2
$$
for all real $x$.