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)

$f\left(x\right)$ is defined if - $log_{1/2} \left(1+\frac{1}{x^{1/ 4}}\right) -1 > 0$
$\Rightarrow \quad log_{1/2} \left(1+\frac{1}{x^{1/ 4}}\right) < -1$
$\Rightarrow \quad1+\frac{1}{x^{1/ 4}} > \left(\frac{1}{2}\right)^{-1}$
$\Rightarrow \quad\frac{1}{x^{1/ 4}} > 1$
$\Rightarrow \quad0 < x < 1$