Question

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.

1. Code the credit card number 3201 2342 3458 0931.

2. A coded credit card number is 2341 0135 7923 0133. What is the original credit card number?

3. Find f(x) if x represents a single input digit. What is the domain
of f(x)?

4. Find f-1(x). What is the domain of f-1(x)?

Answer 1

Can someone help me out please?

Answer 2

I think what I've come up with is correct - let me know either way, please, go to my profile page and send me a message.

As strange as it seems, to decode a number, you do the same thing you do to encode it - you subtract each digit in the encoded number from nine (9)

To encode, you subtract each digit from nine (9)
9999999999
0123456789 - number to be encoded, the digits zero (0) through nine (9), inclusive
-----------------
9876543210 - encoded number, digits subtracted from nine (9)

To decode it, you would also subtract each digit from nine (9)
9999999999
9876543210 - encoded number
----------------
0123456789 - original number, digits subtracted from nine (9)

for encoding and decoding:
if x is one of the set of numbers (0,1,2,3,4,5,6,7,8,9)
f(x) = 9 - x

Domain of f(x) would be, I think, (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

If "f-1(x)" means to take x, a digit of the encoded or decoded number, and subtract it from one (1) the results are shown below, the second column contains the value of x.

1 - 0 - +1
1 - 1 = +0
1 - 2 = -1
1 - 3 = -2
1 - 4 = -3
1 - 5 = -4
1 - 6 = -5
1 - 7 = -6
1 - 8 = -7
1 - 9 = -8

The domain is, I think, -8 to 0 or the set (-8, -7, -6, -5, -4, -3, -2, -1, 0, 1)

Top encode the card number given in (1.), subtract each digit from nine (9)

9999 9999 9999 9999
3201 2342 3458 0931 card number
-------------------------------
6798 7657 6541 9068 encoded number

To decode the card number given in (2), subtract each digit from nine (9)

9999 9999 9999 9999
2341 0135 7923 0133 encoded number
-------------------------------
7658 9864 2076 9866 decoded number

Answer 3

How to use function to solve this question? And it seems a bit unclear for me to find the inverse function @ageta

Answer 4

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.