# Injective function

1. Dec 22, 2009

### m_kosak

who can help me?
ı want to prove this
If f : X → Y is injective and A is a subset of X, then f −1(f(A)) = A.
but how can I do this :(

2. Dec 23, 2009

### CompuChip

So being injective means that whenever f(a) = f(b) in Y, then a = b in X.

The usual proof for such statements is to show two inclusions. Let's start with $f^{-1}(f(A)) \subseteq A$.
Let x be an element of the set on the left hand side. So x is an element in X, for which $x \in f^{-1}(f(A))$. Can you show that x should in fact be an element of A?