For each of the mappings f given in Excercise 1, determine whether f has a left inverse. Exhibit a left inverse whenever one exists

b.

I know the function is one to one and has a left inverse as follows

Based on the lemma we have (lemma 1.24 in our book we know the following)

If there is an element such that , then .

Now I know that is the inverse of the function but is that the inverse only when x is a multiple of 3? and it's an arbitrary for all other conditions? How would I write that ...

A left inverse is

As you can see the problem is essentially solved it's more or less how do I format my answer that would be expected by a professor when I take this course next semester.