Prove: If $\displaystyle f: A \rightarrow B $ is a function and {$\displaystyle {C_\lambda \mid \lambda \epsilon \Lambda}$} is a family of subset of A, then $\displaystyle f$ $\displaystyle ( \bigcup_{\lambda \epsilon \Lambda} C_\lambda )= \bigcup_{\lambda \epsilon \Lambda} f(C_\lambda)$.

I not getting family of subsets. How do I start this off. Assume x belongs to the left side???