- #1

tlkieu

- 8

- 1

**Just wondering if anyone could help me get in the right direction with these questions and/or point me to some material that will help me better understand how to approach these questions**

In what follows I will denote the identity function; i.e. I(x) = x for all x ∈ R.

(a) Show that a function f is surjective if and only if there exists a function g such that f ◦ g = I.

(b) Show that a function f is injective if and only if there exists a function h such that h ◦ f = I.

(c) Suppose f ◦ g = I and h ◦ f = I. Show that g = h.

**Okay so from what I understand for**f ◦ g = I,

**this translates to f(g(x)) = I and for a function to be surjective it means that every element y in Y has element x in X for f(x). So would part (a) involve showing that f is a one-to-one function. I guess my weak point when it comes to these type of questions is setting out logical steps on how to prove, is there a certain system of steps that we follow? Any help would be greatly appreciated!**