Függvényértéke

Függvényértéke, which translates to "function value" in English, refers to the output of a function for a specific input. In mathematics, a function is a rule that assigns a unique output to each input from a given set called the domain. The set of all possible outputs is called the range.

When we write f(x), the 'f' represents the function and 'x' represents the input from the domain. The expression f(x) itself denotes the function value corresponding to the input 'x'. For example, if we have the function f(x) = 2x + 1, and we want to find the function value for the input x = 3, we substitute 3 for x in the function's rule: f(3) = 2(3) + 1 = 6 + 1 = 7. Thus, the function value for x = 3 is 7.

Understanding function values is fundamental to working with functions. It allows us to determine how a function behaves at different points, to plot graphs of functions, and to solve equations and inequalities involving functions. The concept is applicable across various branches of mathematics, from basic algebra to calculus and beyond. Each input in the domain maps to exactly one output in the range, ensuring that the function's behavior is predictable and well-defined.