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.