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# functions question

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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
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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
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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
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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