• 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.
  • Stacey Warren - Expert
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
  • jamiebookeater
I got my questions answered at in under 10 minutes. Go to now for free help!
  • 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.

Looking for something else?

Not the answer you are looking for? Search for more explanations.