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Unformatted text preview: obiahu (vo879) HW13 Schultz (56395) 1 This printout should have 20 questions. Multiplechoice 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 1 1; C. graph of f passes vertical line test. Which properties always ensure that f has an inverse f 1 ? 1. B and C only 2. A and C only 3. A and B only correct 4. none of them 5. B only 6. A only 7. all of them 8. C 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 11 function. Consequently, A. True. B. True. C. False. 002 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 correct 2. 4 8 4 8 4 8 4 8 obiahu (vo879) HW13 Schultz (56395) 2 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 Explanation: The graph of f 1 ( x ) is obtained by reflect ing the graph of f over the line y = x : 4 8 4 8 4 8 4 8 003 10.0 points Find the inverse function, f 1 , for f when f ( x ) = radicalbig 4 x 2 , x 2 . 1. f 1 ( x ) = radicalbig x 2 4 , 2 x 2 2. f 1 ( x ) = radicalbig 4 x 2 , x 2 cor rect 3. f 1 ( x ) = radicalbig 4 x 2 , 2 x 2 4. inverse doesnt exist 5. f 1 ( x ) = 1 4 x 2 , x < 2 Explanation: As the graph 2 2 f = f 1 of f shows, the given f is 11 and so has an inverse. In fact, the graph shows that f 1 = f , but to check this algebraically, we have to solve the equation x = radicalbig 4 y 2 for y . Squaring both sides and simplifying we obtain x 2 = 4 y 2 , i . e ., y 2 = 4 x 2 . Consequently, f 1 ( x ) = radicalbig 4 y 2 , x 2 . 004 10.0 points obiahu (vo879) HW13 Schultz (56395) 3 Find the inverse of f ( x ) = 1 + 9 x 7 4 x . 1. f 1 ( x ) = 7 x 1 9 x + 4 2. f 1 ( x ) = 9 x 1 4 x + 7 3. f 1 ( x ) = 7 x + 1 9 x + 4 4. f 1 ( x ) = 7 x 1 4 x + 9 correct 5. f 1 ( x ) = 7 x + 1 4 x + 9 Explanation: To determine the inverse of f we first solve for x in y = 1 + 9 x 7 4 x . In this case x = 7 y 1 4 y + 9 . The inverse f 1 is now obtained by inter changing x, y . Thus y = f 1 ( x ) = 7 x 1 4 x + 9 . 005 10.0 points If a, b are the solutions of the exponential equation 6 x 2 = 36 x +12 , calculate the value of ab ....
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 Spring '10
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