I am trying to understand a question I got:

Let $U$ be a set.

For every $A\subseteq U$ we define the function: $f\_{A}:P(U) \to P(U)$ such as $f\_{A}(B)=(A\cap B)$.

Prove: $f$ is injective and surjective if and only if $A=U$

First, I do not understand what $f\_{A}$ and $f\_{A}(B)$ mean.

I think that if I will understand this, I will be able to start solving the question.

Any tips will be wonderful!

Thanks!