Final answer:
Fenelon likely sent the letter anonymously to avoid repercussions while giving frank advice to King Louis XIV. We can only speculate on the King's response; he might have considered or ignored the advice, depending on how it aligned with his views and absolute authority.
Step-by-step explanation:
The anonymous letter written by Fenelon to Louis XIV likely remained unsigned due to the sensitive nature of potentially critiquing or advising an absolute monarch who ruled by divine right, as it may have been dangerous or impolite to openly confront the king on matters of governance. This form of sending advice also allowed for the possibility of expressing more frank opinions without direct repercussions to the writer.
As for King Louis XIV's reaction, historical accounts do not provide a definitive answer. However, we can speculate that he may have taken the advice into consideration, or possibly ignored it, especially if it challenged his views or absolute authority. Given Louis XIV's use of art as propaganda and his control over the Royal Academy of Fine Arts, any unsolicited advice may not have been warmly received unless it aligned with his aims and perspectives on rule and power.