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Függvényfüggvény, also known as a composite function, is a function that results from applying one function to the output of another function. In essence, it's a function within a function.
The notation for a composite function is typically written as f(g(x)) or (f ∘ g)(x). This means that
To illustrate, consider two functions: f(x) = x² and g(x) = x + 1.
If we want to find f(g(x)), we substitute g(x) into f(x). So, f(g(x)) = f(x + 1) = (x +
Conversely, if we want to find g(f(x)), we substitute f(x) into g(x). So, g(f(x)) = g(x²) = x² +
Clearly, (x + 1)² ≠ x² + 1 in general.
Composite functions are a fundamental concept in mathematics and have wide-ranging applications in calculus, algebra, and