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.

Question

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 · Answer

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.