1. ## Proof using functions

Let f: A --> B be a function, and suppose that
there is a function g: B --> A such that g circle f is
the identity map on the set A. Prove that f is injective.
(There is a very short proof.)

2. Originally Posted by brudman
Let f: A --> B be a function, and suppose that
there is a function g: B --> A such that g circle f is
the identity map on the set A. Prove that f is injective.
(There is a very short proof.)
Is this true $f(a) = f(b)\, \Rightarrow \,g \circ f(a) = g \circ f(b)?$