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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 \(c\).

 Nov 29, 2018
 #1
avatar+4471 
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\(n=4 \text{ is as far as you can go and has domain }x=\{16\} \\ f_4(16)=0\)

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 Dec 1, 2018
edited by Rom  Dec 1, 2018
 #2
avatar+18 
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I don't think I understand this question, isn't the function fn always defined for [0,1]? Am I missing something?

HelloWorld  Dec 3, 2018
 #3
avatar+4471 
+1

most of the time you end up with the square root of a negative number.

 

for n>4 you always do.

Rom  Dec 3, 2018

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