Set Problems

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• April 21st 2013, 09:34 AM
xmathlover
Set Problems
Using ordered-pair notation, let g be the function defined by
g = {(5n, 3n) | n element of Z}
a) State the domain and a reasonable codomain of g.
b) Evaluate g(10), g(g(50)), and g^-1(-6).

Isn't the domain all real numbers?

How do I go about evaluating and finding the domain and codomain
• April 21st 2013, 09:44 AM
Plato
Re: Set Problems
Quote:

Originally Posted by xmathlover
Using ordered-pair notation, let g be the function dened by
g = f(5n, 3n) | n element of Z
a) State the domain and a reasonable codomain of g.
b) Evaluate g(10), g(g(50)), and g^-1(-6).
Isn't the domain all real numbers?
How do I go about evaluating and finding the domain and codomain

What you have posted leaves a great many questions.

What in the world is the definition of $f(5n,3n)~?$

Do you mean $g(n)=f(5n,3n)~?$.

Where do ordered pairs come in to it at all?

Please repost a meaningful statement.
• April 21st 2013, 09:46 AM
xmathlover
Re: Set Problems
I fixed it.

{5n, 3n | n elements of Z}
• April 21st 2013, 09:54 AM
Plato
Re: Set Problems
Quote:

Originally Posted by xmathlover
I fixed it.

{5n, 3n | n elements of Z}

If $g=\{(5n,3n):n\in\mathbb{Z}\}$ then the domain of $g$ is the set of multiples of five.

The image set (final set or codomain) is the set of multiples of three.

EX: $g(10)=g(5\cdot 2)=3\cdot 2)=6$
• April 21st 2013, 10:03 AM
xmathlover
Re: Set Problems
How did you come to that conclusion? do you look at the ordered pairs as x input, y output?

How would I evaluate g(g(50)) and g^-1(-6)?

g(50) = g(5*10) = 3 * 10 = 30, now how do I run it through the outer g?
• April 21st 2013, 10:33 AM
Plato
Re: Set Problems
Quote:

Originally Posted by xmathlover
How did you come to that conclusion? do you look at the ordered pairs as x input, y output?

How would I evaluate g(g(50)) and g^-1(-6)?

g(50) = g(5*10) = 3 * 10 = 30, now how do I run it through the outer g?

$g(30)=g(5\cdot 6)=3\cdot 6=18$ and $-6=3\cdot ?$ so ?
• April 21st 2013, 10:37 AM
xmathlover
Re: Set Problems
what do you do with the g^-1?
• April 21st 2013, 10:44 AM
Plato
Re: Set Problems
Quote:

Originally Posted by xmathlover
what do you do with the g^-1?

From your questions, it seems that you need a good review of function notation.

$g(g^{-1}(t))=t$. That is if $g^{-1}(t)=s$ then $g(s)=t$

Thus $g^{-1}(-21)=-35$, now can you explain why?
• April 21st 2013, 10:57 AM
xmathlover
Re: Set Problems
you lost me! lol...
• April 21st 2013, 11:03 AM
Plato
Re: Set Problems
Quote:

Originally Posted by xmathlover
you lost me! lol...

I really don't think that you are ready to do these questions.
Why not give your notes and/or textbook a good review?

Asking for $g^{-1}(-21)$ is the same as asking $g(?)=-21$, fill in the blank?
• April 21st 2013, 11:08 AM
xmathlover
Re: Set Problems
for this set {5n, 3n}?

g(7) = -21

wouldn't g^-1(-6) = 2?
• April 21st 2013, 11:11 AM
Plato
Re: Set Problems
Quote:

Originally Posted by xmathlover
for this set {5n, 3n}?

g(7) = -21

No. $g(7)$ does not exist, because seven is not in the domain of $g$. WHY?
• April 21st 2013, 11:13 AM
xmathlover
Re: Set Problems
because it isn't a multiple or 5 or 3?

But by that assumption nothing will work.
• April 21st 2013, 12:05 PM
Plato
Re: Set Problems
Quote:

Originally Posted by xmathlover
because it isn't a multiple or 5 or 3?

But by that assumption nothing will work.

See, as I told you: You do not understand the notation.

$g^{-1}(-21)=-35$. It does work: $g(-35)=-21$.
• April 21st 2013, 12:34 PM
xmathlover
Re: Set Problems
oh so then, g^1(-6) = -10

Is the domain of g express liked this {x | x +- 5} or should it be expressed different? My notes suck...they don't explain anything about domain and codomain in orderpair notation
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