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anonymous
 5 years ago
Inverse of a function help?
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."
a) Code the credit card number 3201 2342 3458 0931.
b) A coded credit card number is 2341 0135 7923 0133. What is the original credit card number?
c) Find f(x) if x represents a single input digit. What is the domain of f(x)?
c) Find f^1(x). What is the domain of f^1(x)?
Note: I have found the answers for both a) and b) already. I just need help with c) and d)...I provided all information given to help.
anonymous
 5 years ago
Inverse of a function help? 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." a) Code the credit card number 3201 2342 3458 0931. b) A coded credit card number is 2341 0135 7923 0133. What is the original credit card number? c) Find f(x) if x represents a single input digit. What is the domain of f(x)? c) Find f^1(x). What is the domain of f^1(x)? Note: I have found the answers for both a) and b) already. I just need help with c) and d)...I provided all information given to help.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Hi juliaj, You're told in the question that each input digit is subtracted from 9, so if x is the input digit, the function would be f(x)=9x. The inverse of a function can be found by the following definition,\[f(f^{1}(x))=x\]where \[f^{1}\] is the inverse of \[f\]Given your equation, the inverse function is then found from \[f(f^{1}(x))=9f^{1}(x)=x\]That is, upon solving for inverse f,\[f^{1}(x)=9x\](it turns out to be the same function). The domain of the inverse is equal to the range of the original function. The original function's range, given it could take xvalues from 0 to 9, was itself, 0m to 9. The inverse function's domain is therefore 0 to 9.
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