For each of the mappings f given in Excercise 1, determine whether f has a left inverse. Exhibit a left inverse whenever one exists
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.
It's modern algebra ... 3000 level or junior level ...
Does anyone know if the above I wrote is actually correct? (the course shouldn't be relevant to if the information is right or not ...)