For security, a credit card number is coded by subtracting each digit from 9. How is the number 3201 2342 3458 0931 coded. What is the card number if the code is 2341 0135 7923 0133.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

For a single input digit x, f(x) = 9- x. The domain of f(x) is [0, 9].

y = f^-1(x) = 9 - x

=> x = 9 - y

=> f^-1(x) = 9 - x

The domain of f^-1(x) is also [0, 9]

 

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The credit card number is coded by subtracting each digit from 9.

The credit card number 3201 2342 3458 0931 is coded as:

(9-3)(9-2)(9-0)(9-1) (9-2)(9-3)(9-4)(9-2) (9-3)(9-4)(9-5)(9-8) (9-0)(9-9)(9-3)(9-1)

=> 6798 7657 6541 9068

If a card number is coded as 2341 0135 7923 0133, the original number is:

(9-2)(9-3)(9-4)(9-1) (9-0)(9-1)(9-3)(9-5) (9-7)(9-9)(9-2)(9-3) (9-0)(9-1)(9-3)(9-3)

=> 7658 9864 2076 9866

lkballer24's profile pic

lkballer24 | Student, Grade 11 | (Level 1) Valedictorian

Posted on

Sorry, I forgot to be specific on this particular question:
  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)?

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