QUESTION: Let f: N₉ N₉ be defined by f(x) = (5x + 3) mod 9. Find f^-1(x) if it exists.

Also, please help me to understand this problem. I would like to learn how to solve more similar problems on my own. My current understanding is this: 1.) f: N₉ N₉ This section of the problem is basically saying that the input of the function will be of the set of natural numbers mod 9, and so will the output, (e.g. {0,1,2,3,4,5,6,7,8}).

2.) We need to determine if (5x + 3) mod 9 is bijective, because if a function is bijective, that means it is invertible. If it is not bijective, that means it is not invertible.

3.) I'm not sure how to actually determine if this is bijective, and how to find the inverse once I actually determine if it even has one.

Thank you for your help.