Thread: Finding inverse function for a mapping with a congruent class

Problem:

F([X]7)=[2x]7

Find the inverse for this function.

So this function maps from x(mod 7) to 2x(mod 7). I was able to prove that the function is one-to-one and onto in a previous function, but I am lost after that.

Am I looking for a function that produces [1]7 when multiplied with [2x]7?


I really would appreciate any and all help.

No, there is no multiplication involved here. You are, as the problem says, looking for the inverse function.

It's not at all difficult to write out exactly what f is:
f(0)= 0, f(1)= 2, f(2)= 4, f(3)= 6, f(4)= 1, f(5)= 3, f(6)= 5.

Therefore, , , , etc.

Originally Posted by alexmahone

This is correct, but how did you go from to ?

Originally Posted by hwill205

This is correct, but how did you go from to ?

So,