1. Let X be the graph of f(x) = p2/3 given below %3D that is, X is the subset of R x R satisfying the given equation. Define a bijective map g : X –→ R. Show that your map g is well-defined, injective, and surjective.
1. Let X be the graph of f(x) = p2/3 given below %3D that is, X is the subset of R x R satisfying the given equation. Define a bijective map g : X –→ R. Show that your map g is well-defined, injective, and surjective.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1C
Transcribed Image Text:1. Let X be the graph of f(x) = x2/3 given below
%3D
that is, X is the subset of R x R satisfying the given equation.
Define a bijective map g : X → R. Show that your map g is well-defined, injective, and surjective.
(b) Declare that a subset A of X is basic if
A = XN B,((x, y))
for some open ball B.((x, y)) = {(a, b) E R × R| V(x – a)² + (y – b)² < c}.
Let Aj and A2 be basic subsets of X.
i. Is Aj U A2 a basic subset of X?
ii. Is A N Az a basic subset of X?
(c) In a similar manner, declare that a subset I of R is basic if
I = RN B(x)
for some open ball B_(x) = {a € R| |r – a| < e}. Given a basic subset A of X, is g(A) a basic
subset of IR? Justify your answer.
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