How to prove $f(A\cap B)=f(A)\cap f(B) \quad \text{for every} \quad A,B⊂X$ when $f: X\rightarrow Y$ is injective?

Question

To prove $f(A\cap B)=f(A)\cap f(B) \Longleftrightarrow \text{f is injective}$

Beginning:

$f(A\cap B)=\{f(x): x\in (A\cap B)\}=\{f(x): x\in A ∧ x\in B\}$ Is that correct and how can I proceed?