$f:(0,2)\to R$$f(x)=\frac{x}{2}+\frac{2}{x}$$g(x)$$\mathrm{g}(\mathrm{x})=\left\{\begin{array}{cc}min\{\mathrm{f}(\mathrm{t})\},& 0<\mathrm{t}\le \mathrm{x}\text{ and }0<\mathrm{x}\le 1\\ \frac{3}{2}+\mathrm{x},& 1<\mathrm{x}<2\end{array}\right.$$g$$x=1$$g$$x\in (0,2)$$g$$x=1$$g$$x\in (0,2)$