The domain of the function f(x)=√(log_10≤ft((5x-x^2)/4)) is

$\log_{10}\left(\frac{5x-x^2}{4}\right)\geq 0⇒\frac{5x-x^2}{4}≥10^0$

$⇒5x-x^2≥4$

$⇒x^2-5x+4≤0$

$⇒(x-4)(x-1)≤0$

$⇒x∈[1,4]$