Set Builder Notation for Domain and Range
Writing the domain and range of a function using the set builder notation is quite helpful. The set of all the values that are input into a function is the domain of the function. For example, the domain of the rational function f(x) = 2/(x-1) would include all real integers other than 1. This is due to the fact that when x = 1, the function f(x) would be undefined. As a result, the domain of this function is written as {x ∈ R | x ≠ 1}.
The set builder notation may also be used to indicate the range of a function. The range of the function is a set of the values that a function can take and for the function f(x) = 2/(x-1) we define the range as,
y = 2/(x-1)
⇒ x – 1 = 2/y
⇒ x = 2/y + 1,
Thus we define the range of function, in the set builder notation as, {y ∈ R | y ≠ 0}.
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Set-Builder Notation
Set-builder Notation is a type of mathematical notation used to describe sets by naming their components or highlighting the requirements that each member of the set must meet. Sets are written in the form of {y | (properties of y)} OR {y : (properties of y)} in the set-builder notation, where the condition that fully characterizes each member of the collection replaces the attributes of y.
The elements and properties are separated using the character ‘|’ or ‘:’ The entire set is interpreted as “the set of all elements y” such that (properties of y), while the symbols ‘|’ or ‘:’ are read as “such that.”
This article explores the set-builder notation, symbols used in set-builder notation, examples, representation of sets methods, etc.
Table of Content
- What is Set-Builder Notation?
- Symbols Used in Set Builder Notation
- Representation of Sets Methods
- Tabular or Roster Form
- Examples of Roster Method
- Set-Builder Notation
- Why Do We Use Set Builder Form?
- How to use a Set Builder Notation?
- How to Write a Set Builder Notation?
- How to read Set Builder Notation?
- Set Builder Notation for Domain and Range
- Set Builder Notation Examples
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