Problem Solving Algebraic Expressions

Problem Solving Algebraic Expressions-32
If a function is defined as in the preceding example, the symbol used for the variable is immaterial; that is, expressions such as: and so on, all define the same function.This is true because if a is any number in the domain of f, then the same image a is obtained no matter which expression is employed. Solution As in Example 1, finding images under f is simply a matter of substituting the appropriate number for x in the expression for f(x).Thus to 3 we assign 9, to - 5 we assign 25, and so on. All the examples of correspondences we have given are functions, as defined below.

Tags: The Things They Carried Essay QuestionsA Systematic Literature Review On Service Description MethodsGrad School Personal StatementFun Homework IdeasBiology Essays Unit 5Short Essay On Eid FestivalHow To Write A Research Topic Proposal

Click "Show Answer" underneath the problem to see the answer.

Or click the "Show Answers" button at the bottom of the page to see all the answers at once.

As another example, to each human being there corresponds a birth date.

To cite a third example, if the temperature of the air is recorded throughout a day, then at each instant of time there is a corresponding temperature.

The element y is called the image of x under f and is denoted by f(x). The range of the function consists of all images of elements of X.

Earlier, we introduced the notation f(x) for the element of Y which corresponds to x.Example 2 Let X denote the set of nonnegative real numbers and let f be the function from X to R defined by for every x in X. Thus: Many formulas which occur in mathematics and the sciences determine functions.As an illustration, the formula A = pi*r, and we may write A= f(r).For each book x in X there corresponds a positive integer y, namely the number of pages in the book.In the second example, if we let X denote the set of all human beings and Y the set of all possible dates, then to each person x in X there corresponds a birth date y. Our examples indicate that to each x in X there corresponds one and only one y in Y; that is, y is unique for a given x.The examples of correspondences we have given involve two sets X and Y.In our first example, X denotes the set of books in a library and Y the set of positive integers.The curved arrows indicate that the elements f(x), f(w), f(z), and f(a) of Y correspond to the elements x, y, z and a of X.Let us repeat the important fact that to each x in X there is assigned precisely one image f(x) in Y; however, different elements of X such as w and z in Figure 1.18 may have the same image in Y. However, f(x) is an element of Y, namely the element which f assigns to x.We sometimes represent correspondences by diagrams of the type shown in Figure 1.17, where the sets X and Y are represented by points within regions in a plane. However, the same element of Y may correspond to different elements of X.The curved arrow indicates that the element y of Y corresponds to the element x of X. For example, two different books may have the same number of pages, two different people may have the same birthday, and so on.

SHOW COMMENTS

Comments Problem Solving Algebraic Expressions

The Latest from chesh.ru ©