210hw4 - x 2 if 1 ≤ x 2 ≤ 5 x 2-5 if 6 ≤ x 2 ≤ 10 x...

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Math 210 Homework 4 Due WEDNESDAY March 9th 1. Let f be the function from N to N defined by f ( x ) = ( 3 x + 1 if x is odd x/ 2 if x is even (a) Is f one-to-one? Why or why not? (b) Is f onto? Why or why not? 2. Let f be the function from Z to Z defined by f ( x ) = x + 2011. Prove that f is a bijection. 3. Let f : R R be defined by f ( x ) = x 3 - 2. Find a formula for the inverse function of f . 4. Let A = { 1 , 2 , 3 , 4 , 5 } . Define f : A A as follows: f ( x ) =
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Unformatted text preview: x 2 if 1 ≤ x 2 ≤ 5 x 2-5 if 6 ≤ x 2 ≤ 10 x 2-10 if 11 ≤ x 2 ≤ 15 x 2-15 if 16 ≤ x 2 ≤ 20 x 2-20 if 21 ≤ x 2 ≤ 25 Express each of the functions f , f ◦ f , and f ◦ f ◦ f as a set of ordered pairs. 1...
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This note was uploaded on 12/07/2011 for the course MATH 210 taught by Professor Staff during the Spring '08 term at University of Delaware.

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