értékhalmazt

értékhalmazt is the Hungarian word for the range of a function. In mathematics, a function can be thought of as a rule that assigns each element of a set, called the domain, to exactly one element of another set, called the codomain. The range of the function is the set of all possible output values that the function can produce.

For example, consider the function f(x) = x^2. If the domain is the set of all real numbers, then the codomain is also the set of all real numbers. However, the range of this function is only the set of non-negative real numbers, because squaring any real number always results in a non-negative number. The notation for the range is often R(f) or Im(f).

Understanding the range of a function is crucial in various areas of mathematics, including calculus, linear algebra, and abstract algebra. It helps in analyzing the behavior and properties of functions, determining their invertibility, and solving equations and inequalities. The concept of the range is also fundamental in understanding mappings between sets and the structure of mathematical objects.