Let there be a function $f:R→R$. Let $A$ & $B$ be two subsets of $R$. From my experience, I know that $f(A∩B)⊆f(A)∩f(B)$.
I don't know how to prove it. Also, are there certain conditions that the function $f$ or the sets $A$ & $B$ should follow for the above condition to be true?