Bounded function

Mathematical function whose set of values is bounded

In mathematics, a function f {\displaystyle f} defined on some set X {\displaystyle X} with real or complex values is called bounded if the set of its values (its image) is bounded. In other words, there exists a real number M {\displaystyle M} such that | f ( x) | ≤ M {\displaystyle |f(x)|\leq M} for all x {\displaystyle x} in X {\displaystyle X} . A function that is not bounded is said to be unbounded.

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