d
(d) \({1 \over 2} \le {\log _{0.1}}x \le 2\)

\({1 \over 2} \le {\log _{0.1}}\,x \Rightarrow {\log _{0.1}}{(0.1)^{1/2}} \le {\log _{0.1}}x\)

\( \Rightarrow \)\({(0.1)^{1/2}} \ge x\) \( \Rightarrow \)\(x \le {1 \over {\sqrt {10} }}\)

\({\log _{0.1}}x \le 2 \Rightarrow {\log _{0.1}}x \le {\log _{0.1}}{(0.1)^2}\)

\(x \ge {(0.1)^2} \Rightarrow x \ge {1 \over {100}}\), \({1 \over {100}} \le x \le {1 \over {\sqrt {10} }}\).

Hence, \({x_{{\rm{max}}}} = {1 \over {\sqrt {10} }},{x_{{\rm{min}}{\rm{.}}}} = {1 \over {100}}\).