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In mathematics, an algebraic function is a function that can be defined as the root of a polynomial equation. Quite often algebraic functions can be expressed using a finite number of terms, involving only the algebraic operations addition, subtraction, multiplication, division, and raising to a fractional power. Common examples of such functions are: f(x)=1/x f(x)=\sqrt{x} f(x)=\frac{ \sqrt{1+x^3}}{x^{3/7}-\sqrt{7} x^{1/3}} Some algebraic functions, however, cannot be expressed by such finite expressions (as proven by Galois and Niels Abel), as is (for example) the function defined by f(x)^5+f(x)^4+x=0.
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