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  4. The domain of the function f(x)= log2 (- log1/2 (1+ (1/x1/4) ) -1) is

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Q. 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

BITSATBITSAT 2014

Solution:

$f (x)$ 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 $
$\Rightarrow 0 < x < 1$