Answer
$ [0, 1] $
Work Step by Step
To find the domain of $f(x)$, first find the domain of the parts then find their intersection
Domain of $ \sqrt{x} $ is $ [0,\infty) $
Domain of $ \sqrt{1-x} $ is $ (-\infty, 1] $
So the domain of $f(x)$ is $ [0,\infty) \cap (-\infty, 1] $ which is $[0,1] $
