Let be a set and f, g: R. Assume max{f(x) + g(x) | x N}, max{f(x)...

Transcribed Image Text:

Let be a set and f, g: R. Assume max{f(x) + g(x) | x N}, max{f(x) | x}, and max{g(x) | x N} exist. (a) Show max{f(x) + g(x) | x N} max{f(x) | x N} + max{g(x) | x N}. (b) Show we can have strict inequality in (a). Let be a set and f, g: R. Assume max{f(x) + g(x) | x N}, max{f(x) | x}, and max{g(x) | x N} exist. (a) Show max{f(x) + g(x) | x N} max{f(x) | x N} + max{g(x) | x N}. (b) Show we can have strict inequality in (a).