# Homework Help: Prove onto

1. Sep 15, 2010

### The Captain

1. The problem statement, all variables and given/known data
Prove that if f: $$X \rightarrow Y$$ is onto, then $$f(f^{-1}(B))=B$$ $$\forall B \in Y$$

2. Relevant equations

3. The attempt at a solution

Last edited: Sep 15, 2010
2. Sep 15, 2010

What does it mean for a function to be onto? What kind of inverse does f possess iff it is onto?

3. Sep 15, 2010

### The Captain

Onto means that for a function $$f:A \rightarrow B$$ if $$\forall b \in B$$ there is an $$a \in A: f(a)=b$$

The inverse means that if you take the $$f^{-1}(b)$$ that it should map back to a?

4. Sep 15, 2010

So I need to prove that if $$f(y)=Y$$ and $$f^{1}(Y)=y$$, that $$f(f^{1}(Y))=Y$$?