First slide

Functions (XII)

Question

The domain of $f (x) = \log |\log x|$ is

Moderate

A

$(0, \infty)$
B

$(0, 1) \cup (1, \infty)$
C

$(1, \infty)$
D

$(- \infty, 1)$

Solution

$f (x) = \log |\log x| . f (x)$ is defined if $|\log x| > 0 and x > 0$ i.e., if
$x > 0 and x \neq 1$ $(|\log x| > 0 if x \neq 1)$
or $x \in (0, 1) \cup (1, \infty)$

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