In: Advanced Math
For part "d" of the question, I know it has asked for mappings f and g such that got is surjective but f is injective, and I have provided that, but the same example is also such that f is also not surjective (to maintain symmetry with part "b").
So, if g°f is an injective function, then so is f.
This is an example where g°f is injective, and g is not injective.
So if g°f is a surjective function, then so is g.
This is an example where g°f is surjective, and f is neither injective nor surjective.