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Math Help - Proving a function is onto.

  1. #1
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    Question Proving a function is onto.

    Hello Everyone,
    I need help with y =2^3-4. To prove it it 1-to 1, onto or both.
    I think I understand how to to prove that the function is one to one.
    2^3-4=2^3-4 then +4 and then divide by 2, so we have x(1)^3=x(2)^3. They are even, if and only if x(1)= x(2) are the same. Therefore this is One to One function.

    What about Onto function y =2^3-4.
    Do I prove it by counterexample? Or otherwise? I can see that it's onto ....but how to write a proof.
    Please someone help me! Thank you.
    Last edited by mr fantastic; October 12th 2011 at 12:50 AM. Reason: Re-titled.
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  2. #2
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    Re: Please someone help me! with ONTO function

    y=2^3-4=5

    (Are you sure you're typing this right?) There is only one value of y. Thus if one value of x satisfies the equation, the equation is onto... however, in this case, every value of y is 5 so it wouldn't be one-to-one.

    If you mean y=x^3-4, this is one-to-one. You just have to prove y = n for some x. (HINT HINT Plug in for y).
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  3. #3
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    Re: Please someone help me! with ONTO function

    Correction. Sorry. Forgot n ^3

    ______________________
    Domain and codomain all real number.

    I need help with f(n) =2n^3-4. To prove it it 1-to 1, onto or both.
    I think I understand how to to prove that the function is one to one.
    2n^3-4=2n^3-4 then +4 and then divide by 2, so we have n(1)^3=n(2)^3. They are even, if and only if n(1)= n(2) are the same. Therefore this is One to One function.

    What about Onto function f(n) =2n^3-4?
    Do I prove it by counterexample? Or otherwise? I can see that it's onto ....but how to write a proof.
    Please someone help me!

    Thank you.
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  4. #4
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    Re: Proving a function is onto.

    Quote Originally Posted by mathproblems View Post
    [FONT=Comic Sans MS]I need help with y=f(x) =2x^3-4. To prove it it 1-to 1, onto or both.
    Please do not use special fonts.
    If f(a)=f(b) then 2a^3-4=2b^3-4.
    If that means that we must have a=b then it is one to one.

    If c\in \mathbb{R} what is f\left( {\sqrt[3]{{\frac{{c + 4}}{2}}}} \right)~?
    Is it onto.
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  5. #5
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    Re: Proving a function is onto.

    Sorry, I dont get it. How is it onto? And why c+4?
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    Re: Proving a function is onto.

    Quote Originally Posted by mathproblems View Post
    Sorry, I dont get it. How is it onto? And why c+4?
    Just evaluate f\left( {\sqrt[3]{{\frac{{c + 4}}{2}}}} \right).

    What do you get?
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  7. #7
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    Re: Proving a function is onto.

    I don't get how you got c+4 and why all of it inside 3 roat. would you please write down transition before f(). Thank you.

    If I evaluate, I plug 1 or -1, result is a real number. Then it's onto.
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  8. #8
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    Re: Proving a function is onto.

    Quote Originally Posted by Plato View Post
    Please do not use special fonts....
    What's the problem? Soroban does it - I would be shocked if he didn't in any future post...
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  9. #9
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    Re: Proving a function is onto.

    Quote Originally Posted by TheChaz View Post
    What's the problem? Soroban does it - I would be shocked if he didn't in any future post...
    I do not reply to or edit his posts. I find is distracting when replying.
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  10. #10
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    Re: Proving a function is onto.

    what Plato is getting at is this:

    the way you show a function is onto, is show if you pick any old point in the co-domain, you can find some point in the domain that maps to it.

    since the co-domain is the real numbers, if we want to prove it is onto, we must find, for every real number c,

    a real number x with f(x) = c. Plato has given you a BIG hint on what this x might be.
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  11. #11
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    Re: Proving a function is onto.

    Quote Originally Posted by mathproblems View Post
    Sorry, I dont get it. How is it onto? And why c+4?
    Do you not see that f\left( {\sqrt[3]{{\frac{{c + 4}}{2}}}} \right)=c~?.
    Never mind where it comes from.
    That proves that given any c\in\mathbb{R} there is a real number that is mapped to c.
    So the function is onto.

    Now for from it came.
    If c=2x^3-4 can you solve for x~?
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  12. #12
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    Re: Proving a function is onto.

    Quote Originally Posted by Plato View Post
    I do not reply to or edit his posts. I find is distracting when replying.
    Indeed, once I tried to parse a quote of his in my reply... I learned that my LaTex skills are far inferior!
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  13. #13
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    Re: Proving a function is onto.

    I am trying to get better at at...I really want to understand how f of 3 roat appeared...;-(
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    Re: Proving a function is onto.

    Quote Originally Posted by mathproblems View Post
    I am trying to get better at at...I really want to understand how f of 3 roat appeared...;-(
    Are you saying that you cannot solve c=2x^3-4 for x~?
    If so, there is no wonder you are having difficulty with This.
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  15. #15
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    Re: Proving a function is onto.

    yes, this is what I am saying. I went to school 25 years ago...now I don't remember some things. And now I am taking discrete math ...
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