Compute the domain of the real-valued function \( f(x)=\sqrt{1-\sqrt{2-\sqrt{x}}}.\)

Lightning
Jul 24, 2018

#1**+1 **

We can solve this by inspection

Note that when x = 1 the expression under the entire radical is 0

And x cannot be smaller than this (note if it were, for example, 0, 1 - √2 under the radical would be negative

And x cannot be larger than 4 because [2 - √x ] would result in a negative quantity under a radical

So...the domain is [ 1, 4 ]

Here's a graph : https://www.desmos.com/calculator/xxzra4wyai

CPhill
Jul 24, 2018