Question

The domain of the function $\varphi \left(x\right)={\log }_7\left(-{\log }_{\frac{1}{2}}\left(1+\frac{1}{\sqrt[4]{4x}}\right)-1\right)$ is

• A. $[x:1<x<2]$
• B. $[x:0<x<1]$
• C. $[x:0<x<2]$
• D. $[x:1<x<3]$

Answer 1

Answer: (B)

$[x:0<x<1]$

$\varphi \left(x\right)=lo{g}_7(-lo{g}_{1/2}(1+\frac{1}{\sqrt[4]{4x}})-1)$ is

$\Rightarrow lo{g}_{1/2}(1+\frac{1}{\sqrt[4]{4x}})<-1$

$\Rightarrow 1-\frac{1}{\sqrt[4]{4x}}>(2^{-1}{)}^{-1}=2$

$\Rightarrow \frac{1}{4\sqrt{x}}>1;0<x<1$

Hence Domain is $[x:0<x<1]$