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

 Jun 10, 2021
 #1
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Square root cannot be negative  

   so for the first part   sqrt (x)   the domain is    x >= 0

       then it is subtracted from two and squre 'rooted' again ....cannot be negative

               so x must be between 0  and   4   inclusive

 

    then it is added to 1 before taking the square root again....if the previous step was positive or zero, this will be too...

 

[ 0 , 4 ]

 Jun 10, 2021

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