# Algebraic and Non-Algebraic Functions

A function is called an **algebraic function** if it can be constructed using algebraic operations (such as addition, subtraction, multiplication, division, and taking roots) on polynomials.

Any rational function is automatically an algebraic function.

For example, `f(x)=sqrt(1/x)` , `f(x)=(x^2+1/x)/(root(3)(x^2+1/x^2)+x^4+1)` .

Functions that are not algebraic are called **transcedental**.

The set of transcendental functions includes the trigonometric, inverse trigonometric, exponential, and logarithmic functions, but it also includes a vast number of other functions that have never been named (for example, functions that are defined as sum of infinite series).