Question

Find the domain of definition of the following function:
$y=\sqrt{{\log }_{0.4}(x-x^2)}$

Answer 1

${\log }_{0.4}(x-x^2)\ge 0$

As the base is less than $1$

$0<x-x^2\le 1$

$x^2-x<0x(x-1)<0x\in (0,1)$ and $x^2-x+1\ge 0D=1-4\times 1=-3\left(alwaysposiitive\right)$

Hence, $x\in (0,1)$