Questions about what is an onto function and what is not

1. Jul 13, 2004

relinquished™

onto or not?

Hello ^_^

I just have a few questions regarding onto functions. I'm a student studying BS Math here in the Phils. Right now i have a subject concerning math logic, and before we study the subject proper, my professor is discussing the basics of relations an functions ^_^;;; So if this question is misplaced Im truly sorry ^^;;;

In my previous quiz, there was a question that asked "State whether the given function is onto or not:

Domain = [-4,4], f(x) = x^2
Domain = [-1,1], f(x) = sin x

My understanding of an onto function is that it is a function wherein all the members of the codomain of the function should be assigned to at least one value of x in the domain. I answered that "yes, f(x)=x^2 is an onto function" because all the values of x in the domain have a corresponding y, i.e., there is no undefined value for any value of x or y. The next question's answer was was the same. However, when I asked for clarifications on what were the correct answers, my professor said that these two functions were not onto. Can someone please tell me why?

Last edited: Jul 13, 2004
2. Jul 13, 2004

AKG

:rofl:
Check out this Wikipedia article. Based on what's in that article, I don't understand how you can answer that function either way because there is no co-domain specified. The answer is yes to the first question if and only if the co-domain is a subset of [0,16]. The answer to the second question is yes if and only if the co-domain is a subset of [sin(-1), sin(1)].

3. Jul 15, 2004

relinquished™

Thanks for the clarifications ^_^

4. Jul 30, 2004

DrMatrix

The co-domain for the function in the first question cannot be a proper subset of [0,16] or you would not have a function. Where you said "is a subset of" should be replaced with "equals" for both questions.

5. Jul 30, 2004

gravenewworld

Yes I don't see how you can answer that question. The values that the function maps to must be specified in order for you to answer the question.

6. Jul 30, 2004

AKG

What makes you say this? It's definitely a function. Check out that wikipedia link for what an "onto function" is for clarification. I believe I understood it correctly.

7. Jul 30, 2004

Muzza

I don't think it has anything to do with the function being onto or not. Can you exhibit a proper subset S of [0, 16] such that f: [-4, 4] -> S, f(x) = x^2 is a function? Remember,

So (for example) f: [-4, 4] -> [0, 4] won't work since then f(3) = 9 would be in [0, 4].

Last edited: Jul 30, 2004
8. Jul 30, 2004

AKG

Muzza you're right.