grandes-ecoles 2023 Q44

grandes-ecoles · France · centrale-maths1__official Sequences and Series Properties and Manipulation of Power Series or Formal Series
We fix $\alpha > 0$ and define the function $W$ from $\mathbb{K}[X]$ by $$W : \begin{array}{ccc} \mathbb{K}[X] & \rightarrow & \mathbb{K}[X] \\ p & \mapsto & p(\alpha X) \end{array}$$
Show that $W$ is an automorphism of $\mathbb{K}[X]$.
We fix $\alpha > 0$ and define the function $W$ from $\mathbb{K}[X]$ by
$$W : \begin{array}{ccc} \mathbb{K}[X] & \rightarrow & \mathbb{K}[X] \\ p & \mapsto & p(\alpha X) \end{array}$$

Show that $W$ is an automorphism of $\mathbb{K}[X]$.