2011 AMC 12A Problem 21

Let f_{1}(x)=\sqrt{1-x}, and for integers n \geq 2, let f_{n}(x)=f_{n-1}(\sqrt{n^2 - x}). If N is the largest value of n for which the domain of f_{n} is nonempty, the domain of f_{N} is \{ c\}. What is N+c?

\textbf{(A)}\ -226 \qquad \textbf{(B)}\ -144 \qquad \textbf{(C)}\ -20 \qquad \textbf{(D)}\ 20 \qquad \textbf{(E)}\ 144

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.