anonymous
  • anonymous
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.
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Hi 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)=9-x. 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 \[f(f^{-1}(x))=9-f^{-1}(x)=x\]That is, upon solving for inverse f,\[f^{-1}(x)=9-x\](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 x-values from 0 to 9, was itself, 0m to 9. The inverse function's domain is therefore 0 to 9.

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