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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
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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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
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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