Problem: The multiplication of real numbers are functions mult: R x R to R, where mult(x,y)=xy. Is mult one-to-one? Is it onto?
Just think for a moment about the first part. You don't even have to leave the natural numbers. What is 6*4 and what is 8*3? What does that say about * being 1 to 1? As for onto, try to think of a single real number that is not the product of two real numbers, What is 1*x for any x at all?
These sound like the kind of questions that some books put in to make you think so that you can check if you grasp the concept that the author is trying to explain. You are not helping yourself if you do not try to work this kind of question out for yourself. It is better to get this kind of question wrong after trying it for yourself than just to turn to a forum without trying for yourself first. After all, suppose I had answered Yes, No to your questions how would you know whether my answer could be trusted?
Sorry if this is a harsh response to your first post - but I think you will often get more from the forum if you use it as a way of learning about interesting questions than a way to learn an answer.
I appreciate your reply, but I am trying to learn. That is why I joined this forum. Sometimes it does help to see a problem answered in order to learn it. I hav a grasp on the concepts of one-to-one and onto, as I have solved other problems with them in it. The wording on this problem was a bit strange. I appreciate your help.
If you have joined the forum to learn then you have come with the right attitude. I am not a good mathematician as my thinking is very concrete, but I hope my answer shows that sometimes a hard conceptual question can be answered with facts that you know very well already. More abstract mathematical concepts should be there to help you generalise what you know to new situations, not to confuse about something you did already know.
Good luck with your future posts!