4x9. Let f : R – {2} → R – {–4} be defined by f(x) :=2 - x(a)Prove that f is bijective.Find a formula for f-(x) (you may use your work from part(b)(a) if you'd like).(c)and R - {-4}?What does part (a) tell you about the cardinalities of R – {2}

Answered: Image /qna-images/answer/4d90c31d-7404-440d-92a3-2c3039d6cc8a.jpg

4x 9. Let f : R – {2} → R – {–4} be defined by f(x) = 2 - x (a) Prove that f is bijective. Find a formula for f-1(x) (you may use your work from part (b) (a) if you'd like). (c) and R- {-4}? What does part (a) tell you about the cardinalities of R – {2}

4x 9. Let f : R – {2} → R – {–4} be defined by f(x) = 2 - x (a) Prove that f is bijective. Find a formula for f-1(x) (you may use your work from part (b) (a) if you'd like). (c) and R- {-4}? What does part (a) tell you about the cardinalities of R – {2}

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 32E

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Question

4x
9. Let f : R – {2} → R – {–4} be defined by f(x) :
=
2 - x
(a)
Prove that f is bijective.
Find a formula for f-(x) (you may use your work from part
(b)
(a) if you'd like).
(c)
and R - {-4}?
What does part (a) tell you about the cardinalities of R – {2}

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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.
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