Answer:
Function notation is a simpler method of describing a function without a lengthy written explanation. The most frequently used function notation is f(x) which is read as “f” of “x”. In this case, the letter x, placed within the parentheses and the entire symbol f(x), stand for the domain set and range set respectively.
Step-by-step explanation:
The concept of functions was developed in the seventeenth century when Rene Descartes used the idea to model mathematical relationships in his book Geometry. The term “function” was then introduced by Gottfried Wilhelm Leibniz fifty years later after publication of Geometry.
Later, Leonhard Euler formalized the usage of functions when he introduced the concept of function notation; y = f (x). It was until 1837 when Peter Dirichlet – a German mathematician gave the modern definition of a function.
Functions - Function Notation
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What is a Function?
In mathematics, a function is a set of inputs with a single output in each case. Every function has a domain and range. The domain is the set of independent values of the variable x for a relation or a function is defined. In simple words, the domain is a set of x-values that generate the real values of y when substituted in the function.
On the other hand, the range is a set of all possible values that a function can produce. The range of a function can be expressed in interval notation or inform of inequalities.
What is a Function Notation?
Notation can be defined as a system of symbols or signs that denote elements such as phrases, numbers, words etc.
Therefore, function notation is a way in which a function can be represented using symbols and signs. Function notation is a simpler method of describing a function without a lengthy written explanation.
The most frequently used function notation is f(x) which is read as “f” of “x”. In this case, the letter x, placed within the parentheses and the entire symbol f(x), stand for the domain set and range set respectively.
Although f is the most popular letter used when writing function notation, any other letter of the alphabet can also be used either in upper or lower case.
Advantages of using function notation
Since most functions are represented with various variables such as; a, f, g, h, k etc., we use f(x) in order avoid confusion as to which function is being evaluated.
Function notation allows to identify the independent variable with ease.
Function notation also helps us to identify the element of a function which has to be examined.
