First slide

Functions (XII)

Question

The domain of the following function is
$f (x) = \log_{2} (- \log_{1 / 2} (1 + \frac{1}{x^{1 / 4}}) - 1)$

Difficult

A

$(0, 1)$
B

$(0, 1]$
C

$[1, \infty)$
D

$(1, \infty)$

Solution

$\begin{array}{l} f (x) is defined if \\ - \log_{1 / 2} (1 + \frac{1}{x^{1 / 4}}) - 1 > 0 \\ or \log_{1 / 2} (1 + \frac{1}{x^{1 / 4}}) < - 1 \\ or 1 + \frac{1}{x^{1 / 4}} > {(\frac{1}{2})}^{- 1} \\ or \frac{1}{x^{1 / 4}} > 1 \\ or 0 < x < 1 \end{array}$

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