Question

Find the domain of definition of the following function:
$f\left(x\right)={\log }_2(-{\log }_{1/2}(1+\frac{6}{\sqrt[4]{4x}})-2)$

Answer 1

$x>0-{\log }_{1/2}(1+\frac{6}{\sqrt[4]{4x}})-2>0-{\log }_{1/2}(1+\frac{6}{\sqrt[4]{4x}})>2(1+\frac{6}{\sqrt[4]{4x}})>{\left(\frac{1}{2}\right)}^{-2}1+\frac{6}{\sqrt[4]{4x}}>42^4>xx<16Also,1+\frac{6}{\sqrt[4]{4x}}>06>-\sqrt[4]{4x}{6}^4>xx<6^4$

Taking intersection, we get

$x\in (0,16)$