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## Main Question or Discussion Point

Stumped on a couple of questions, if anyone could help!

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

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