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