2. The figure below represents the set X = (R – {0}) U {A, B} where A and B are two points not on the real line. A (a) Define f : X → R by Jo if x e {A, B} |x otherwise. f(x) = i. Is f injective? Prove or provide a counterexample. ii. Is f surjective? Prove or provide a counterexample. (b) For any two positive reals c < d, define IA(-c, d) = (-c, 0)U{A}U (0, d) IB(-c, d) = (-c, 0) U{B}U (0, d). i. Determine Y = U IA(-1/c, 1/d) and compute f(Y). c,dER>o ii. Determine Z = n IB(-1/c, 1/d) and compute f(Z). c,dER>o
2. The figure below represents the set X = (R – {0}) U {A, B} where A and B are two points not on the real line. A (a) Define f : X → R by Jo if x e {A, B} |x otherwise. f(x) = i. Is f injective? Prove or provide a counterexample. ii. Is f surjective? Prove or provide a counterexample. (b) For any two positive reals c < d, define IA(-c, d) = (-c, 0)U{A}U (0, d) IB(-c, d) = (-c, 0) U{B}U (0, d). i. Determine Y = U IA(-1/c, 1/d) and compute f(Y). c,dER>o ii. Determine Z = n IB(-1/c, 1/d) and compute f(Z). c,dER>o
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
PB 1
Transcribed Image Text:2. The figure below represents the set X = (R – {0}) U {A, B} where A and B are two points not
on the real line.
A
(a) Define f : X → R by
Jo if x € {A, B}
f (x) =
otherwise.
i. Is f injective? Prove or provide a counterexample.
ii. Is f surjective? Prove or provide a counterexample.
(b) For any two positive reals c < d, define
IA(-c, d) = (-c, 0) U{A}U (0, d)
IB(-c, d) = (-c, 0) U{B}U (0, d).
i. Determine Y
U IA(-1/c, 1/d) and compute f(Y).
c,deR>o
ii. Determine Z =
IB(-1/c, 1/d) and compute f(Z).
c,dER>o
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