# Proof using functions

• Nov 15th 2009, 01:21 PM
brudman
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.)
• Nov 15th 2009, 01:25 PM
Plato
Quote:

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 $f(a) = f(b)\, \Rightarrow \,g \circ f(a) = g \circ f(b)?$