Let \(f_{1}(x)=\sqrt{1-x}\), and for integers \(n \geq 2\), let \(f_{n}(x)=f_{n-1}\sqrt{n^2 - x})\). 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 \(c\).
+6251 \(n=4 \text{ is as far as you can go and has domain }x=\{16\} \\ f_4(16)=0\)
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+25 I don't think I understand this question, isn't the function fn always defined for [0,1]? Am I missing something?
