Answer
$(0,1]$
Work Step by Step
1. $f(x)=\frac{(1-x)^2}{\sqrt x}-4\sqrt x(x-1)\geq0$
$f(x)=\frac{x^2-2x+1-4x^2+4x}{\sqrt x}=-\frac{3x^2-2x-1}{\sqrt x}$
$f(x)=-\frac{(3x+1)(x-1)}{\sqrt x}\geq0$
2. The denominator $\sqrt x$ requires that $x\gt0$, the term $3x+1$ will be positive, and
the only requirement would be $-(x-1)\geq0$ or $x\leq1$
3. The solution would be $(0,1]$
