What is Algebraic Function?
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.
Examples of such functions are:
Some algebraic functions, however, cannot be expressed by such finite expressions (this is Abel–Ruffini theorem). This is the case, for example, of the Bring radical, which is the function implicitly defined by[fusion_builder_container hundred_percent=”yes” overflow=”visible”][fusion_builder_row][fusion_builder_column type=”1_1″ background_position=”left top” background_color=”” border_size=”” border_color=”” border_style=”solid” spacing=”yes” background_image=”” background_repeat=”no-repeat” padding=”” margin_top=”0px” margin_bottom=”0px” class=”” id=”” animation_type=”” animation_speed=”0.3″ animation_direction=”left” hide_on_mobile=”no” center_content=”no” min_height=”none”]
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In more precise terms, an algebraic function of degree n in one variable x is a function y= 
where the coefficients ai(x) are polynomial functions of x, with coefficients belonging to a set S. Quite often, 
A function which is not algebraic is called a transcendental function, as it is for example the case of 
As an equation of degree n has n roots, a polynomial equation does not implicitly define a single function, but n functions, sometimes also called branches. Consider for example the equation of the unit circle: 
An algebraic function in m variables is similarly defined as a function y which solves a polynomial equation in m + 1 variables:
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