At school, I did a Chinese-English translation assignment and translated one of the sentences into English as follows:
He is always willing to take on whatever task assigned to him.
And my teacher changed "whatever" to "any" as in:
He is always willing to take on any task assigned to him.
I asked a friend who is a native-speaker of English for advice, and he said I could use "whatever" as long as I also used "is" behind "task":
He is willing to take on whatever task is assigned to him.
I understand that "whatever" can be a conjunction, a pronoun, and a determiner. It seems that my friend treats "whatever task is assigned to him" as a noun clause that functions as the object of preposition "on." I can understand this explanation.
However, my question lies in whether it is proper to use "whatever" as a determiner in this sentence. I know that both "any" and "whatever" can be determiners. When analyzing a sentence like "He is always willing to take on any task assigned to him," I think that the noun phrase "any task" is modified by a reduced adjective clause:
He is always willing to take on any task (which/that is) assigned to him.
If my reasoning stands, I can use "whatever" as a determiner before the noun "task" and use a reduced adjective clause to modify the noun phrase "whatever task":
He is always willing to take on whatever task (which/that is) assigned to him.
Is my reasoning correct? I would appreciate it very much if you can tell me what you think. Thank you!