függvényösszetétel

Függvényösszetétel, often translated as function composition, is a mathematical operation that takes two functions and produces a new function. The output of the first function becomes the input of the second function. If we have two functions, f and g, the composition of f with g is denoted as f ∘ g, which is read as "f composed with g". The resulting function (f ∘ g)(x) is defined as f(g(x)). This means we first apply the function g to the input x, and then we apply the function f to the result of g(x).

The domain and range of the composed function are important. The domain of (f ∘ g) consists of all x in the domain of g such that g(x) is in the domain of f. The range of (f ∘ g) is the set of all values f(y) where y is in the range of g and y is in the domain of f. Function composition is not necessarily commutative, meaning that (f ∘ g)(x) is generally not equal to (g ∘ f)(x). The order in which the functions are applied matters. This operation is fundamental in many areas of mathematics, including calculus and abstract algebra.