The domain of the function \(f(x)=\sqrt{\log_{10}\left(\frac{5x-x^2}{4}\right)}\) is

\([0,5]\) \([1,4]\) \([1,2]\) \([0,1]\)

\([1,4]\)

$\log_{10}\left(\frac{5x-x^2}{4}\right)\geq 0⇒\frac{5x-x^2}{4}≥10^0$ $⇒5x-x^2≥4$ $⇒x^2-5x+4≤0$ $⇒(x-4)(x-1)≤0$ $⇒x∈[1,4]$