ALGEBRAIC FUNCTION Meaning and
Definition
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An algebraic function is a function that can be expressed as the combination of algebraic operations such as addition, subtraction, multiplication, division, and raising to a power, using only algebraic expressions. It is defined as a function that satisfies a polynomial equation between its variables and coefficients.
In simpler terms, an algebraic function is a mathematical equation or expression that relates two or more variables and can be solved using algebraic techniques. These functions involve polynomial functions, rational functions, and several other types of functions constructed from algebraic operations.
For example, the function f(x) = 3x^2 + 2x - 1 is an algebraic function since it consists of algebraic terms like x raised to a power, constants, and coefficients, and is constructed using algebraic operations such as multiplication and addition. Similarly, functions like g(x) = (x^3 + 2x)/(x + 1) and h(x) = √(4x - 3) are also algebraic functions since they are constructed using algebraic operations and involve polynomial and rational expressions.
Algebraic functions are fundamental in algebra, as they allow us to model and solve various mathematical and real-life problems involving relationships between variables. These functions are extensively used in fields like physics, economics, engineering, and computer science to analyze and predict behaviors, make calculations, and solve equations.
Etymology of ALGEBRAIC FUNCTION
The word "algebraic" originates from the Arabic term "al-jabr", which was the title of a mathematics book written by the Persian mathematician Al-Khwarizmi in the 9th century. This book introduced the concept of solving equations using symbolic manipulations. Over time, "al-jabr" became "algebra" in English.
The term "function" has Latin roots and comes from the word "functio", which means "performance" or "execution". It was first used in mathematics in the 17th century to describe a relationship between two variables.
When combined, the term "algebraic function" refers to a function that can be constructed using algebraic operations, such as addition, subtraction, multiplication, division, and taking roots.
