Lecture_16 - MA1100 Lecture 16 Functions Rules of functions...

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1 MA1100 Lecture 16 Functions Rules of functions Domain and Codomain Image and Preimage Range Equality of functions
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MA1100 Lecture 16 2 MT Question 3 (a) A = {0, « }. Write down P(A). Ans: Common mistake:
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MA1100 Lecture 16 3 MT Question 3 (b) If C Œ A B, then C A = C B Common mistake: Let x œ C. Then x œ A B. Then x œ A and x œ B. Then x œ C Aa n d x œ C B. So C A = C B
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MA1100 Lecture 16 4 MT Question 4 (a) A 1 A 2 in terms of congruence modulo 6 Common mistake: A n = {m œ Z + | (n+1) | m } A 1 = {m œ Z + | 2 | m } A 2 = {m œ Z + | 3 | m } Then A 1 A 2 = {m œ Z + | 6 | m } 2 | m and 3 | m 6 | m
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MA1100 Lecture 16 5 MT Question 4 (b) Show A 1 A 3 = A 1 Common mistake 1: A 3 = {m œ Z + | m ª 1, 2, 3, 5 mod 6} A 3 = {m œ Z + | 4 | m } Common mistake 2: To prove A 1 A 3 Œ A 1 and A 1 Œ A 1 A 3 Note: No need to prove A 1 A 3 Œ A 1 A n = {m œ Z + | (n+1) | m }
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MA1100 Lecture 16 6 MT Question 4 Common mistake 1: Common mistake 2: (c) Find A n n A n = A 1 A 2 A n n n terms Should be: contains m not divisible by 2, 3, 4, … A n = « n Should be: A n = {1} n Common mistake 3: Prove m 2, 3, 4, … and conclude A n = {1} n A n = {m œ Z + | (n+1) | m }
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MA1100 Lecture 16 7 Functions Which of the following are functions? 1. f(x) = sin x 2. f(x) = x 2 3. f(x) = 1/x 4. f(x) = absolute value of x 5. f(x) = square root of x
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MA1100 Lecture 16 8 Functions Definition A function from a set A to a set B is a rule that associate with every element x of A exactly one element of the set B. set A set B x y A function is also call a mapping. rule Domain Codomain The set A is called the domain of the function. The set B is called the codomain of the function.
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MA1100 Lecture 16 9 Functions A function from a set A to a set B is a special type of relation from A to B.
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This note was uploaded on 03/19/2012 for the course SCIENCE MA1100 taught by Professor Forgot during the Fall '08 term at National University of Singapore.

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Lecture_16 - MA1100 Lecture 16 Functions Rules of functions...

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