Question 28
Let $f : [0, \infty) \to [0, \infty)$ be a differentiable function, with continuous derivative, and $f(f(x)) = x^2$, for every $x \in [0, \infty)$. Prove that
$$
\int_{0}^{1} (f'(x))^2 \, dx \ge \frac{30}{31}.
$$
$$
\int_{0}^{1} (f'(x))^2 \, dx \ge \frac{30}{31}.
$$