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Question
The domain of definition of the function f(x) = log |x| is
Options
(a) R
(b) (−∞, 0)
(c) (0, ∞)
(d) R − {0}
Solution
(d) R − {0}
f(x) = log |x|
\[\text{ For f(x) to be defined,} \]
\[\left| x \right| > 0, \text{ which is always true . } \]
\[\text{ But } \left| x \right| \neq 0\]
\[ \Rightarrow x \neq 0\]
\[\text{ Thus, dom }(f) = R - {0} . \]
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