calc13 - pokharel(yp624 – HW13 – Radin –(56520 1 This...

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Unformatted text preview: pokharel (yp624) – HW13 – Radin – (56520) 1 This print-out should have 21 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Consider the following properties that a func- tion f might have: A. f ′ ( x ) ≥ 0 for all x ; B. f is an even function; C. graph of f passes horizontal line test. Which properties always ensure that f has an inverse f − 1 ? 1. none of them 2. C only correct 3. B and C only 4. A only 5. B only 6. A and C only 7. all of them 8. A and B only Explanation: A function f has an inverse, often denoted by f − 1 , when there exists a function g so that g ( f ( x )) = x, f ( g ( x )) = x ; then f − 1 = g . Such a function g exists if and only if (i) the graph of f passes the horizontal line test; (ii) the graph of f is strictly increasing or strictly decreasing; (iii) f is a 1-1 function. Consequently, A. False ( f could be constant). B. False, ( f is not 1-1). C. True. 002 10.0 points Consider the following functions: F 1 ( x ) = | x + 1 | ,- 1 ≤ x ≤ 1 , F 2 ( x ) = sin 2 x,- π/ 4 ≤ x ≤ π/ 4 , F 3 ( x ) = x 2 + 2 x,- 1 ≤ x ≤ 1 . Which have an inverse on the given domain? 1. F 2 only 2. F 1 only 3. F 1 and F 3 only 4. all of them correct 5. F 2 and F 3 only 6. none of them 7. F 1 and F 2 only 8. F 3 only Explanation: A function f has an inverse, f − 1 , when any one of the following conditions are satisfied: (1) it is a 1-1 function on its domain, (2) its graph passes the horizontal line test, (3) it is either strictly increasing or strictly decreasing. Consequently, A. Have: ( f ( x ) = x + 1 on domain, so f is strictly increasing). B. Have: (is 1-1). C. Have: ( f strictly increasing on given do- main). pokharel (yp624) – HW13 – Radin – (56520) 2 003 10.0 points Suppose f is a 1-1 function with domain A and range B. What is the range of f − 1 ? 1. Can’t be determined. 2. B 3. A correct Explanation: The domain of a function is the range of its inverse, and vice-versa . 004 10.0 points If the graph of f is 4 8- 4- 8 4 8- 4- 8 which of the following is the graph of f − 1 ( x )? 1. 4 8- 4- 8 4 8- 4- 8 2. 4 8- 4- 8 4 8- 4- 8 3. 4 8- 4- 8 4 8- 4- 8 4. 4 8- 4- 8 4 8- 4- 8 5. 4 8- 4- 8 4 8- 4- 8 correct Explanation: The graph of f − 1 ( x ) is obtained by reflect- ing the graph of f over the line y = x : pokharel (yp624) – HW13 – Radin – (56520) 3 4 8- 4- 8 4 8- 4- 8 005 10.0 points If f − 1 is the inverse of f , determine the value of f ( f − 1 (4)). 1. f ( f − 1 (4)) = 16 2. f ( f − 1 (4)) = 4 correct 3. f ( f − 1 (4)) = 1 16 4. f ( f − 1 (4)) = 1 4 5. Need to know f Explanation: The inverse, f − 1 , of f has the property that f ( f − 1 ( x )) = x, f − 1 ( f ( x )) = x ....
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This note was uploaded on 06/05/2010 for the course PHYS 92515 taught by Professor Tsoi during the Spring '10 term at University of Texas.

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calc13 - pokharel(yp624 – HW13 – Radin –(56520 1 This...

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