Question 91
Determine if there exist functions $f, g: \mathbb{R} \to \mathbb{R}$ satisfying for every $x \in \mathbb{R}$ the following equations
$$
f(g(x)) = x^3 \quad \text{and} \quad g(f(x)) = x^2.
$$
$$
f(g(x)) = x^3 \quad \text{and} \quad g(f(x)) = x^2.
$$