Question 96
Let $g : \mathbb{R} \to \mathbb{R}$ be a continuous, decreasing function, such that $g(\mathbb{R}) = (-\infty, 0)$. Prove that there are no continuous functions $f : \mathbb{R} \to \mathbb{R}$ such that the equality $f \circ f \circ \dots \circ f = g$ is true for some integer $k \ge 2$.