Let $f:X\rightarrow Y$. Let $A$, $A\_1$ and $A\_2$ be subsets of $X$ and $B$, $B\_1$, and $B\_2$ be subsets of $Y$. Then, I need to prove that $f^{-1}(B\_1\cup B\_2)=f^{-1}(B\_1)\cup f^{-1}(B\_2)$.

I know that by the definition of an inverse image, if we let $x\in f^{-1}(B\_1\cup B\_2)$, then we know that $f^{-1}(x)\in(B\_1\cup B\_2)$. 
From here, I'm not sure how to get to $f^{-1}(B\_1)\cup f^{-1}(B\_2)$.