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 \(c\).

Guest Nov 29, 2018

#1

#2**+2 **

I don't think I understand this question, isn't the function f_{n} always defined for [0,1]? Am I missing something?

HelloWorld
Dec 3, 2018