Algebraic function

Mathematical function

In mathematics, an algebraic function is a function that satisfies a polynomial equation. Thus an equation of the following form holds: a n ( x) f ( x) n + a n − 1 ( x) f ( x) n − 1 + ⋯ + a 1 ( x) f ( x) + a 0 ( x) = 0 {\displaystyle a_{n}(x)f(x)^{n}+a_{n-1}(x)f(x)^{n-1}+\cdots +a_{1}(x)f(x)+a_{0}(x)=0} where the a k ( x) {\displaystyle a_{k}(x)} are polynomials (not all zero). Basic examples of algebraic functions are polynomial functions, rational functions, the nth root function, and functions obtained from these by composition and algebraic operations (addition, multiplication, subtraction, and division).

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