Some general advice for asking questions on this site: 1) It is better to ask single question in one post. (Your post contains 4 different questions.) 2) It is good to search before asking. (I'd guess that there already are some posts about this on this site.) 3) It is good to explain your terminology. (The last part mention total function. Does this mean that in the first three subquestions you can possible work with partial functions?) See also: How to ask a good question? — Martin Sleziak 9 mins ago

For the parts dealing with injective functions you can have a look at these past questions: math.stackexchange.com/questions/63552/… or math.stackexchange.com/questions/229065/… or math.stackexchange.com/questions/845284/… math.stackexchange.com/questions/442510/… — Martin Sleziak 7 mins ago

For the parts dealing with surjective functions, you can have a look at: math.stackexchange.com/questions/777132/… math.stackexchange.com/questions/229065/… math.stackexchange.com/questions/1274914/… math.stackexchange.com/questions/75880/… and perhaps also math.stackexchange.com/questions/1705016 — Martin Sleziak 2 mins ago