Find the Domain of \( \log|x| \)
Question:
The domain of definition of the function
\[ f(x)=\log|x| \]
is
(a) \(R\)
(b) \((-\infty,0)\)
(c) \((0,\infty)\)
(d) \(R-\{0\}\)
Solution:
For logarithmic function,
\[ |x|>0 \]
This is true for all real values except
\[ x=0 \]
Therefore, domain is
\[ R-\{0\} \]
\[ \boxed{\text{Correct Answer: (d)}} \]