Question

The domain of the function $f\left(x\right)={\log }_2\left(-{\log }_{1/2}\left(1+\frac{1}{x^{1/4}}\right)-1\right)$ is

• A. (0, 1)
• B. (0, 1]
• C. $[1,\infty )$
• D. $(1,\infty )$

Answer 1

Answer: (A)

$f(x)$ is defined if
$-{\log }_{1/2}\left(1+\frac{1}{x^{1/4}}\right)-1>0$
$\Rightarrow {\log }_{1/2}\left(1+\frac{1}{x^{1/4}}\right)<-1$
$\Rightarrow 1+\frac{1}{x^{1/4}}>{\left(\frac{1}{2}\right)}^{-1}$
$\Rightarrow \frac{1}{x^{1/4}}>0$
$\Rightarrow 0<x<1$