Answer to Question #34185 in Real Analysis for lia_pratiwi

Question

Let X be a nonempty set and let f: X-> R have bounded ranges in r. if a element R. show that : sup {a + f(x): x element X} = a + sup {f(x): x element X} .Show that we also have inf {a+f(x) : x element X} = a+ inf {f(x): x element X}