f: A→B, g: B→A
Is g ° f defined? If so, what is its domain and range?
To determine if g ° f, the composition of g and f, is defined, we need to check if the codomain of f matches the domain of g. In this case, the codomain of f is B and the domain of g is also B. Therefore, g ° f is defined.
The domain of g ° f is the domain of f, which is A. The range of g ° f is the range of g, which is A.
So, g ° f is defined, and its domain is A and its range is A.