Determine whether a function is one-to-one and/or onto?

Question

Specifically, what needs to be shown for a function to be one-to-one and what makes it 'onto'?

example: f(x)=  x/ [(x+2)(x-2)]

and f: (-2,2)=>R (all real numbers)

The hint is let u be in R and find an x that is an element of (-2,2) such that  f(x)=u

Thanks for any advice.

Anonymous · Accepted Answer

let f:A-->B
a function is said to be 1-1 if for all f(a)=f(a') then a=a'
meaning each element has a unique image under f 

a funciton is onto if for every b in B there exists an a in A such that f(a)=b

there is no theorem to prove in your question if you post one I can help you more

? · Answer

Onto Function Test

Anonymous · Answer

I don't know what "onto" means.  A function is one to one if it passes the vertical line test.  That means that when you graph the function, and you draw a vertical line, that vertical line will intersect with your graph at only one point at any given position on the graph.  You can email me about "onto" if you want, I'll give it a shot but frankly I've never heard of it.

Edit: I have to pull out my book...Does this answer help? otherwise, it's beyond my schooling.  Sorry. http://answers.yahoo.com/question/index?qid=20080901215852AAJ1RQ7

? · Answer

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Determine whether a function is one-to-one and/or onto?

4 Answers