In a paper I'm writing, I end a proof with a displayed equation that has some cases in it. The relevant code looks something like the following:
\[f(x) = \begin{cases}
2x & \text{if $x<0$}\\
7 & \text{if $x=0$}\\
1-x & \text{if $x>0$}
\end{cases} \]
\end{proof}
What I want to happen is for the amsthm "tombstone" to be placed on the right-hand side of the page aligned with the "1-x" line. I think this should be possible by placing a \qedhere in an appropriate place, but I can't seem to figure out where (I've tried all the obvious choices, and they all give me incorrect behavior).
Thanks for any help!

