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answer item 2 only under question

answer item 2 only under question

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.1: Inverse Functions
Problem 56E
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answer item 2 only under question 1
1. Let X be the graph of f(r) = r given below that is. X is the subset of R x R satisfying the given equation. 1 Define a bijective map g : X → R. Show that your map g is well-defined, injective, and surjective. 2 Declare that a subset A of X is basic if A = Xn B,((r. y)) for some open ball B,((r. 4)) = {(a,b) € R x R| V - a)² + (y – b)? < c}. Let Aj and A, be basic subsets of X. i. Is Aj U Az a basic subset of X? ii. Is A, nA, a basic subset of X? 3 In a similar manner, declare that a subset / of R is basic if I = RN B,(r) for some open ball B,(r) = {a € R| |r – a| < e}. Given a basic subset A of Y, is g(A) a basic subset of R? Justify your answer.
Transcribed Image Text:1. Let X be the graph of f(r) = r given below that is. X is the subset of R x R satisfying the given equation. 1 Define a bijective map g : X → R. Show that your map g is well-defined, injective, and surjective. 2 Declare that a subset A of X is basic if A = Xn B,((r. y)) for some open ball B,((r. 4)) = {(a,b) € R x R| V - a)² + (y – b)? < c}. Let Aj and A, be basic subsets of X. i. Is Aj U Az a basic subset of X? ii. Is A, nA, a basic subset of X? 3 In a similar manner, declare that a subset / of R is basic if I = RN B,(r) for some open ball B,(r) = {a € R| |r – a| < e}. Given a basic subset A of Y, is g(A) a basic subset of R? Justify your answer.
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