Final answer:
The question regarding a bijection function f and a new function g cannot be fully answered due to critical information being missing, namely the definition of function g. The provided analog with gazintz, gazatz, and garingers illustrates logical transitivity, which could relate to functions if properly defined.
Step-by-step explanation:
The student's question seems to imply a scenario where a function f is defined from the Cartesian product of a set A with itself (A x A) to the set A, and the question further mentions a bijection, which is a function that is both one-to-one and onto. The question then introduces a new function g with an incomplete definition and asks for proof related to this new function.
However, the question seems to be missing critical parts, particularly the definition of the function g. Without this definition, it's not possible to proceed with the proof directly.
To illustrate a concept analogous to the question, if we look at a logical sequence of statements like All gazintz are gazatz, and All gazatz are garingers, then according to the rules of logic, it follows that All gazintz are garingers.
This principle of transitivity can be applied when dealing with sets and functions if all the premises are known and properly defined. But for a detailed answer to be given, the full definition of function g and what is to be proven about it must be provided.