Domain of f(x) = | x| is - Vidyadip

MCQ

Domain of $f(x) = \log |\log x|$ is

A
$(0,\;\infty )$
B
$(1,\;\infty )$
✓
$(0,\;1) \cup (1,\;\infty )$
D
$( - \infty ,\;1)$

✓

Answer

Correct option: C.

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

c
(c) $f(x) = \log |\log x|$, $f(x)$ is defined if $|\log x| > 0$ and $x > 0$

$i.e.,$ if $x > 0$ and $x \ne 1$

==> $x \in (0,\,1) \cup (1,\,\infty ).$

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