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

Guest Jun 10, 2021

#1**+2 **

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 ]

ElectricPavlov Jun 10, 2021