Let $F$ be the vector subspace of $E$ formed of polynomial functions. For $k \in \mathbb{N}$, we denote by $p_k$ the function defined by $p_k(x) = x^k$. For all $k \in \mathbb{N}$, calculate $T(p_k)$. Deduce that $F$ is stable under $T$.
Let $F$ be the vector subspace of $E$ formed of polynomial functions. For $k \in \mathbb{N}$, we denote by $p_k$ the function defined by $p_k(x) = x^k$.
For all $k \in \mathbb{N}$, calculate $T(p_k)$. Deduce that $F$ is stable under $T$.