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. 6798 7657 6541 9068.
2. 7658 9864 2076 9866.
3. and domain of f(x) is {0,1,2,3,4,5,6,7,8,9}.
4. and domain of f⁻¹(x) is {0,1,2,3,4,5,6,7,8,9}.
We are given that,
The coding method for the card number is 'Subtract each digit from 9'.
So, we have,
Part 1: The number given is 3201 2342 3458 0931.
So, after subtracting each digit from 9, we have,
The coded number is 6798 7657 6541 9068.
Part 2: The coded number given is 2341 0135 7923 0133.
To find the original number, we will subtract the digits from 9.
The original number is 7658 9864 2076 9866.
Part 3: We have f(x), where x represents the single input digit.
That is, 'x' can have values from {0,1,2,3,4,5,6,7,8,9}.
As, the coded output is the number subtracted from 9.
We get, the function is.
So, the domain of f(x) is {0,1,2,3,4,5,6,7,8,9}.
Part 4: We need to find the inverse function.
So, we have, i.e. .
Thus, the inverse function is
Since, the range of f(x) is the domain of f⁻¹(x).
The domain of f⁻¹(x) is {0,1,2,3,4,5,6,7,8,9}.
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