Examples for $\max\{f(x)+g(x)\}\leq \max{f(x)}+ \max{g(x)}$ and $\min\{f(x)+g(x)\}\geq\min{f(x)}$+min{g(x)}. Can someone give me an example with concrete functions for the following relations $\max\{f(x)+g(x)\}\leq \max{f(x)}+ \max{g(x)}$ and $\min\{f(x)+g(x)\}\geq \min{f(x)}+\min{g(x)}$? I suppose one example would be enough to verify both.

Another solution: $f(x)=g(x)=0$ (or equal to any other constants)
