Compute the domain of the real-valued function\(f(x)=\sqrt{3-\sqrt{5-\sqrt{x}}}. \)
x must be ≥ 0
And 5 - sqrt x must be ≥ 0
So
5 - sqrt x ≥ 0
5 ≥ sqrt x square both sides
25 ≥ x
So.....the domain is
[ 0 , 25 ]
See the graph here : https://www.desmos.com/calculator/gxk17ddz6u
