Representation Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Write the solution set of x2=9x^2 = 9 in (a) roster notation, (b) set-builder notation.

Solution

  1. 1
    Solve: x2=9⇒x=±3x^2 = 9 \Rightarrow x = \pm 3.
  2. 2
    (a) Roster: {−3,3}\{-3, 3\}.
  3. 3
    (b) Set-builder: {x∈R:x2=9}\{x \in \mathbb{R} : x^2 = 9\}.

Answer

(a)  {−3,3},(b)  {x∈R:x2=9}(a)\;\{-3,3\},\quad (b)\;\{x \in \mathbb{R} : x^2 = 9\}
Both representations describe the same two-element set. The set-builder form emphasises the defining property while the roster form lists the elements explicitly.

About Representation

A mathematical representation is any format — diagram, equation, table, graph, or symbolic expression — used to encode and communicate a mathematical idea or relationship between quantities.

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More Representation Examples

Example 1 easy

Represent the set [formula] with [formula] and [formula] using three different representations: (1)

Example 2 medium

The inequality [formula] can be represented as an absolute value inequality, a compound inequality,

Example 4 medium

A function [formula] triples its input. Represent [formula] as (a) a formula, (b) a table for inputs

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