2. Let fixey and giY-2 bo arbitrary maps of suts (a) Show that it f and I are injuctive so is the composition of got then (b) Show that if f- and I are surjective is the composition of gof. tion so (C) Show that if I and so is the thon so is (gof) = f'og are bijective tion g of and 9 composi
2. Let fixey and giY-2 bo arbitrary maps of suts (a) Show that it f and I are injuctive so is the composition of got then (b) Show that if f- and I are surjective is the composition of gof. tion so (C) Show that if I and so is the thon so is (gof) = f'og are bijective tion g of and 9 composi
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
![2. Let fixsy and giY-Z bo arbitrary
maps of suts
are injective
so is the composition of got
9
(a) Show that if f and
then
(b) Show that if f.and I are surjective
is the composition of gof.
tion
So
9₁
() show that if I and
are bijective
thon so is the composition gof and
(gof) = f'og
(d) show that fixgy is injective iff
there exists hit sx such that hof= idx
(@) Show that fixsy is surjective iff
there exists hil ex such that
for cidy, Ro only if part requires the
ation of choice](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca708747-373f-4dbe-b127-10492ca0e68f%2F8a674c7b-0ebe-4aa7-a676-43996f8e261e%2Fhrloju_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Let fixsy and giY-Z bo arbitrary
maps of suts
are injective
so is the composition of got
9
(a) Show that if f and
then
(b) Show that if f.and I are surjective
is the composition of gof.
tion
So
9₁
() show that if I and
are bijective
thon so is the composition gof and
(gof) = f'og
(d) show that fixgy is injective iff
there exists hit sx such that hof= idx
(@) Show that fixsy is surjective iff
there exists hil ex such that
for cidy, Ro only if part requires the
ation of choice
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