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(a) How many pairs (f, g) E F x F are there so that go f(1) = 1? Explain.

(a) How many pairs (f, g) E F x F are there so that go f(1) = 1? Explain.

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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Can you elaborate part a?And I don’t understand why for g we have 4^3 choices
3. Let A = {1,2, 3, 4}. Let F be the set of all functions from A to A. (a) How many pairs (f, g) E F × F are there so that go f(1) = 1? Explain. (b) How many pairs (f, g) E F × F are there so that gof(1) = 1 and go f(2) (c) How many pairs (f, g) E F × F are there so that go f(1) = 1 or go f(2) = 2? Explain. (d) How many pairs (f, g) E F x F are there so that go f(1) ±1 or go f(2) + 2? Explain. 2? Explain.
Transcribed Image Text:3. Let A = {1,2, 3, 4}. Let F be the set of all functions from A to A. (a) How many pairs (f, g) E F × F are there so that go f(1) = 1? Explain. (b) How many pairs (f, g) E F × F are there so that gof(1) = 1 and go f(2) (c) How many pairs (f, g) E F × F are there so that go f(1) = 1 or go f(2) = 2? Explain. (d) How many pairs (f, g) E F x F are there so that go f(1) ±1 or go f(2) + 2? Explain. 2? Explain.
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