Question

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

(a) R
(b) (−∞, 0)
(c) (0, ∞)
(d) R − {0}

Answer 1

(d) R − {0}

f(x) = log |x|
$$\begin{gathered} \mathrm{For}f\left(x\right)\mathrm{to}\mathrm{be}\mathrm{defined}, \\ \left|\mathrm{x}\right|>0,\mathrm{which}\mathrm{is}\mathrm{always}\mathrm{true}. \\ \text{But}\left|\mathrm{x}\right|\ne 0 \\ \Rightarrow \mathrm{x}\ne 0 \\ \mathrm{Thus},\mathrm{dom}\left(\mathrm{f}\right)=\mathrm{R}-\left\{0\right\}. \end{gathered}$$