The domain of definition of the function f(x) =
Question:

The domain of definition of the function f(x) = log |x| is

(a) R

(b) (−∞, 0)

(c) (0, ∞)

(d) R − {0

Solution:

(d) R − {0}

f(x) = log |x|

For $f(x)$ to be defined,

$|\mathrm{x}|>0$, which is always true.

But $|x| \neq 0$

$\Rightarrow x \neq 0$

Thus, $\operatorname{dom}(\mathrm{f})=\mathrm{R}-\{0\}$.