Prove a Function is OntoUse the definition of onto to prove that the given function is onto.Let f:R → R with f(x) = 3(x - 4)

Answered: Image /qna-images/answer/6196b749-8fde-45d4-9cda-e38075d80958.jpg

Answered: Prove a Function is Onto Use the…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 26E: 26. Let and. Prove that for any subset of T of .

See similar textbooks

Similar questions

15. a. Show that the mapping given in Example 2 is neither onto nor one-to-one. b. For this mapping , show that if , then . c. For this same and , show that .
27. Let , where and are nonempty. Prove that has the property that for every subset of if and only if is one-to-one. (Compare with Exercise 15 b.). 15. b. For the mapping , show that if , then .
If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?
A relation R on a nonempty set A is called asymmetric if, for x and y in A, xRy implies yRx. Which of the relations in Exercise 2 areasymmetric? In each of the following parts, a relation R is defined on the set of all integers. Determine in each case whether or not R is reflexive, symmetric, or transitive. Justify your answers. a. xRy if and only if x=2y. b. xRy if and only if x=y. c. xRy if and only if y=xk for some k in . d. xRy if and only if xy. e. xRy if and only if xy. f. xRy if and only if x=|y|. g. xRy if and only if |x||y+1|. h. xRy if and only if xy i. xRy if and only if xy j. xRy if and only if |xy|=1. k. xRy if and only if |xy|1.
Give an example of mappings and such that one of or is not onto but is onto.
6. a. Give an example of mappings and , different from those in Example , where is one-to-one, is onto, and is not one-to-one. b. Give an example of mappings and , different from Example , where is one-to-one, is onto, and is not onto.
26. Let and. Prove that for any subset of T of .
A Function f is a rule that assigns to each element x in a set A exactly ________ element(s) called f(x) in a set B. Which of the following tables defines y as a function of x ?

Recommended textbooks for you

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

Calculus For The Life Sciences

Calculus

ISBN:

9780321964038

Author:

GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:

Pearson Addison Wesley,

College Algebra

Algebra

ISBN:

9781938168383

Author:

Jay Abramson

Publisher:

OpenStax

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

Calculus For The Life Sciences

Calculus

ISBN:

9780321964038

Author:

GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:

Pearson Addison Wesley,

College Algebra

Algebra

ISBN:

9781938168383

Author:

Jay Abramson

Publisher:

OpenStax

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

College Algebra

Algebra

ISBN:

9781305115545

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

Prove a Function is Onto Use the definition of onto to prove that the given function is onto. Let f:R → R with f(x) = 3(x - 4)