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Find the domain of the function \[f(x)=\sqrt{1-\sqrt{2+\sqrt{3+\sqrt{x}}}}.\]

 May 6, 2024
 #1
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I don't think it is possible to achieve a real number from this function. 

 

This is because \(\sqrt{2}\) is greater than 1, so in order for it to be real, we would need \(\sqrt{3+\sqrt{x}}\) to be negative, which obviously is not possible...

 

I think the domain is essentially just \([0, \infty)\)

 

Thanks!

 May 6, 2024

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