Question

Write the interval for which the function f(x) = 1/x is strictly decreasing .

Answer 1

$$\begin{gathered} \mathrm{When}{\mathrm{x}}_1,{\mathrm{x}}_2>0 \\ {\mathrm{x}}_1>{\mathrm{x}}_2 \\ \mathrm{f}\left({\mathrm{x}}_1\right)<\mathrm{f}\left({\mathrm{x}}_2\right) \\ \mathrm{So}, \\ \mathrm{f}\left(\mathrm{x}\right)\mathrm{is}\mathrm{strictly}\mathrm{decreasing}\mathrm{in}\left(0,\infty \right) \\ \mathrm{When}{\mathrm{x}}_1,{\mathrm{x}}_2<0 \\ {\mathrm{x}}_1>{\mathrm{x}}_2 \\ \mathrm{f}\left({\mathrm{x}}_1\right)<\mathrm{f}\left({\mathrm{x}}_2\right) \\ \mathrm{So}, \\ \mathrm{f}\left(\mathrm{x}\right)\mathrm{is}\mathrm{strictly}\mathrm{decreasing}\mathrm{in}\left(-\infty ,0\right) \\ \mathrm{Therefore},\mathrm{f}\left(\mathrm{x}\right)\mathrm{is}\mathrm{strictly}\mathrm{decreasing}\mathrm{in}\left(-\infty ,0\right)\cup \left(0,\infty \right). \end{gathered}$$