# 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, $$${f{{\left({x}\right)}}}=\sqrt{{\frac{{1}}{{x}}}}$$$, $$${f{{\left({x}\right)}}}=\frac{{{{x}}^{{2}}+\frac{{1}}{{x}}}}{{{\sqrt[{{3}}]{{{{x}}^{{2}}+\frac{{1}}{{{x}}^{{2}}}}}}+{{x}}^{{4}}+{1}}}$$$.

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).