Bereichsmenge
Bereichsmenge is a term used in mathematics to denote the set of all actual outputs produced by a function. It is commonly referred to as the image or range of the function. The concept is distinct from the domain (Definitionsmenge) of inputs and the codomain (Zielmenge) of possible outputs; the Bereichsmenge is a subset of the codomain consisting of all values that the function attains.
Formally, let f be a function with domain D and codomain C. The Bereichsmenge, or Bildmenge, of
Examples help illustrate the concept:
- f: ℝ → ℝ, f(x) = x^2. The domain is ℝ, the codomain is ℝ, and the Bereichsmenge is [0, ∞).
- f: [0,1] → ℝ, f(x) = sin(πx). The Bereichsmenge is [0, 1].
- f: ℝ → ℝ, f(x) = 2x + 1. The Bereichsmenge is ℝ.
- The term Bereichsmenge appears as a synonym for Bildmenge or Wertebereich in some texts, but usage
- The Bereichsmenge depends on both the domain and the codomain chosen for the function; changing either
- The Bereichsmenge is central to discussions of surjectivity and to solving equations of the form f(x) =