Thread: Help!: Consider two functions f: X ->Y and g: Y->X where X and Y are two finite sets.

I need some help with these questions from my textbook that I know these questions will be on an upcoming quiz and I am having difficulty with.

Consider two functions f: X ->Y and g: Y->X where X and Y are two finite sets.

g○f = 1x

Argue by either providing a detailed proof or counter example.

a) Does necessarily f○g = 1y?
b) Is f, g necessarily one-one?
c) Is f, g necessarily onto?

Can someone help me out here?