Would someone please help me with the answer to this question please:

(it is a prep question for the qualifier and taken from an old exam)

Assume a function f: A->B and sets A1, A2 $\displaystyle \subseteq$ A, for which f(A1 $\displaystyle \cap$ A2) $\displaystyle \neq$ f(A1)$\displaystyle \cap$ f(A2).

Demonstrate this inequality.