"This duty is very important to me."
Translation:Bu görev benim için çok önemli.
Sometimes the difference is very minimal or non-existent. In other cases, it is dramatic. Here is a dramatic example: "he gave his life to me" vs "he gave his life for me".
A medicine can be very important for me, for my health. It affects my life directly. Sleeping is also important for me. For my beauty. Something else may be important in my head, in my thinking. It is important morally, on principle, etc. Without having a direct effect on my life. Saving the snow leopard from extinction is important to me. TO me. Even though it makes no difference in my personal life whatsoever.
The line between "to" and "for" is blurry in most cases, in my opinion. :)
No, it is not a compound world. Actually most of Turkish people don't know where this word comes from and i have just learned also. I've looked at the dictionaries and the answer of your question is that: The verb görmek is takes the suffix -(e)v and görmek means "iş görmek" here. (i do not know how i should translate this verb, maybe to work). Hope this helps.