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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.
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).
Correction. Sorry. Forgot n ^3
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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.
Please do not use special fonts.Quote:
Originally Posted by mathproblems
[FONT=Comic Sans MS]I need help with. To prove it it 1-to 1, onto or both.
Ifthen
.
If that means that we must havethen it is one to one.
Ifwhat is
Is it onto.
Sorry, I dont get it. How is it onto? And why c+4?
Just evaluateQuote:
Originally Posted by mathproblems
.
What do you get?
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.
What's the problem? Soroban does it - I would be shocked if he didn't in any future post...Quote:
Originally Posted by Plato
I do not reply to or edit his posts. I find is distracting when replying.Quote:
Originally Posted by TheChaz
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.
Do you not see thatQuote:
Originally Posted by mathproblems
.
Never mind where it comes from.
That proves that given anythere is a real number that is mapped to c.
So the function is onto.
Now for from it came.
Ifcan you solve for
Indeed, once I tried to parse a quote of his in my reply... I learned that my LaTex skills are far inferior!Quote:
Originally Posted by Plato
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 solveQuote:
Originally Posted by mathproblems
If so, there is no wonder you are having difficulty with This.
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 ...