Q42 / 125 · BITSAT 2014 · Mathematics

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

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

Solution

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

Hence, the correct answer is option: 'A'.

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