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

 Jul 24, 2018

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


cool cool cool

 Jul 24, 2018
edited by CPhill  Jul 24, 2018

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