Let X be a nonempty set and let f : X → R have bounded range in R. If a ∈ R, show that Example 2.4.l(a) implies that
Sup{a + f(x) : x ∈ X} = a + sup{f(x) : x ∈ X}:
Show that we also have
Inf{a + f(x) : x ∈ X} = a + inf{f(x) : x ∈ X}: