Question 93
Find all functions $f : \mathbb{R} \setminus \{0\} \to \mathbb{R}$ so that
$$
f\left(\frac{1}{x}\right) \ge 1 - f(x) \ge x^2 f(x)
$$
for all $x \in \mathbb{R} \setminus \{0\}$.
$$
f\left(\frac{1}{x}\right) \ge 1 - f(x) \ge x^2 f(x)
$$
for all $x \in \mathbb{R} \setminus \{0\}$.