# Word Problem Credit card

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1. Dec 17, 2004

### aisha

For security, a credit card number is coded in the following way, so that it can be sent as a message. "Subtract each digit from 9"

code the credit card number 3201 2342 3458 0931

I dont understand the subtract each digit from 9 is that to code or uncode? Also for the above code the credit card what do I do to each number? do I add 9 or subtract 9?

I have another credit card number that is already coded, to find the original card number do i subtract each number from 9?

2. Dec 17, 2004

### dextercioby

I believe it's pretty clear.It gives a credit card number and askes for the coded version.It should be:6798 7657 6541 9068.
Simple subtraction from 9999 9999 9999 9999.
The uncoding is simple:again subtraction from that "99..."number.

Daniel.

3. Dec 17, 2004

### Staff: Mentor

Does it make a difference? Try it and see.

4. Dec 17, 2004

### aisha

How come we subtract by 9 to uncode and code?

5. Dec 17, 2004

### dextercioby

I guess you haven't read the post/problem very carefully.It mentions "Subtract each digit from 9".So the problem tells you how to code.As Doc depicted,it makes no difference between coding and uncoding.Both are made through the same opperation.Subtraction of each digit from 9.

Daniel.

6. Dec 17, 2004

### aisha

ok my coded credit card number for 3201 2342 3458 0931 is
6798 7657 6541 9068
my original credit card number for another credit card 2341 0135 7923 0133 is
7658 9864 2076 9866

the question says find f(x) if x represents a single input digit. What is the domain of f(x)

and find^-1(x) what is the domain of f^-1(x)?

I dont know how to find f(x) and the inverse? What do I do? The inverse is probably all the numbers backwards but which set of numbers am I using?

7. Dec 17, 2004

### dextercioby

The function is $f:\{0,1,2,3,4,5,6,7,8,9}\rightarrow \{0,1,2,3,4,5,6,7,8,9}\$

$$f(x)=9-x.$$

Find the inverse and its domain.

Daniel.
What numbers backwards?????? :surprised

8. Dec 17, 2004

### aisha

lol sorry no numbers backwards. if f(x)=9-x then is the domain {x:x<=9,XER}?
and is the inverse of this (x-9)/-1? If so then is the domain of the inverse {x:x>=9,XER}?

9. Dec 17, 2004

### dextercioby

I've already told u what the function and its domain are.The inverse it's easy to find.And its domain can be seen from ISS. :tongue2:
By "XER",do you mean:$x\in R$ ??If so,then it's wrong,the digits are natural numbers.

Daniel.

10. Dec 17, 2004

### aisha

:tongue2: well is my inverse wrong? I dont know the notation for not real numbers :P ahhh HELP ME PLZ

11. Dec 17, 2004

### dextercioby

As both I and Doc figured decades ago,the inverse coincides with the function.They share both the domain and the range.That is all digits from 0 till 9.
Hope it's clear.

Daniel.

12. Dec 17, 2004

### aisha

Lol thanks a lot but u said it wasnt real numbers natural numbers, what is the notation for that? Also (x-9)/-1 can I leave the inverse like that? Or can it be simplified to -(x-9)?

13. Dec 17, 2004

### dextercioby

1.Check the posts again.I haven't used the expression "real numbers",but "natural numbers",because digits are natural numbers.
2.$$f(x)=9-x ;f^{-1} (x) =9-x$$
Wasn't it obvious from what i said?????? :surprised

Daniel.

14. Dec 17, 2004

### aisha

LOL WHAT AM I SAYING:P IM SAYING THAT U SAID THEY WERE NATURAL NUMBERS SOOOO IF ITS NOT XER THEN WHAT iS IT???? WHAT DO I WRITE IN THE BRACKETS {} lol UR SOOO FUNNY OMG :tongue2: and is the inverse (x-9)/-1? if so is that the same as -(x-9)

N+?

Last edited: Dec 17, 2004
15. Dec 17, 2004

### dextercioby

ROFL :rofl: :rofl: :rofl: :rofl: :rofl: :rofl: :rofl:
You're incredible..................................... :tongue2:

I already told you what to put between those brackets.Hell,i've been trying myself,but i just couldn't... :tongue2: Only 2 '{' instead of 4 (chack post no.7,two paranthesis missing ).
I already told you the inverse was the same function:9-x.It is the same with -(x-9),but why the hell write it like that??

Daniel.

16. Dec 17, 2004

### aisha

LOL :rofl: :rofl: :rofl: :rofl: OMG I JUST REALIZED THAT THEY ARE THE SAME FUNCTION, ahhh lol and yes ur right y the hell would I write it like that -(x-9) and the domain is the same for both too , hhmmmmm so here this is what im gonna right now lol dont freak if this is still wrong {x:x<=9,N+} domain for f(x) and inverse? or or or {x:0,1,2,3,4,5,6,7,8,9} is that what u want me to write :tongue2: Cant u just write it out properly once :!!) plzzzzzzz lol :tongue2: DEXTERCIOBY ??? WHERE ARE U Someone please say something please.

Last edited: Dec 17, 2004
17. Dec 17, 2004

### dextercioby

1.I'm in my room.
2.Though it's not in the spirit of this help forum,i'll write the answer:
$$f:A\rightarrow A ,A=\{x\in N,x\leq 9$$},
$$f(x)=9-x$$
$$f^{-1}:A\rightarrow A, f^{-1} (x)=9-x$$

Is everything clear,FINALLLLLLLLLLLLLLLLLLLLLLLLLLLYYYYYYYYYY :tongue2: ??

Daniel.

PS.Anyway,i give up.It's no longer funny... :tongue2:

18. Dec 18, 2004

### Gokul43201

Staff Emeritus
Just one little point here...since the Naturals don't include 0, it would be better to say that x belongs to the Whole Numbers (W?).

19. Dec 18, 2004

### aisha

lol so XEW? instead of XEN?

20. Dec 18, 2004

### dextercioby

You're in Canada,he's in US and i'm in Belgium.We have different views about the sets of numbers.For me,natural numbers (N) include 0.If i wanna say that zero is excluded,i write (N*).
I was too surprised to learn that the Americans use N (natural numbers),W (whole numbers) & i can't remember what they use for {...,-3,-2,-1,0,1,...} or the negative axis.I find his weird.
Advice:to avoid confusions and unnecessary complications simply write
{0,1,...,9} or without the dots:{0,1,2,3,4,5,6,7,8,9}. :tongue2:

Daniel.

EDIT:I'd use BMW if i were u... :tongue2:

Last edited: Dec 18, 2004