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Let $f_{1}(x)=\sqrt{1-x}$, and for integers $n \geq 2$, let$f_{n}(x)=f_{n-1}\left(\sqrt{n^2 - x}\right).$Let $N$ be the largest value of $n$ for which the domain of $f_n$ is nonempty. For this value of $N,$ the domain of $f_N$ consists of a single point $\{c\}.$ Compute $c.$

Oct 4, 2020