This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: mandel (tgm245) HW13 Radin (56470) 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. graph of f passes vertical line test; B. f ( x ) 0 for all x ; C. f is 1 1. Which properties always ensure that f has an inverse f 1 ? 1. C only correct 2. all of them 3. B only 4. none of them 5. A only 6. B and C only 7. A and C only 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 11 function. Consequently, A. False. B. False ( f could be constant). C. True. 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 mandel (tgm245) HW13 Radin (56470) 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 25 x 2 , x 5 . 1. f 1 ( x ) = radicalbig 25 x 2 , x 5 correct 2. inverse doesnt exist 3. f 1 ( x ) = radicalbig x 2 25 , 5 x 5 4. f 1 ( x ) = 1 25 x 2 , x < 5 5. f 1 ( x ) = radicalbig 25 x 2 , 5 x 5 Explanation: As the graph 5 5 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 25 y 2 for y . Squaring both sides and simplifying we obtain x 2 = 25 y 2 , i . e ., y 2 = 25 x 2 . Consequently, f 1 ( x ) = radicalbig 25 y 2 , x 5 . 004 10.0 points mandel (tgm245) HW13 Radin (56470) 3 Find the inverse of f ( x ) = 1 + 9 x 5 4 x . 1. f 1 ( x ) = 5 x + 1 9 x + 4 2. f 1 ( x ) = 5 x + 1 4 x + 9 3. f 1 ( x ) = 9 x 1 4 x + 5 4. f 1 ( x ) = 5 x 1 9 x + 4 5. f 1 ( x ) = 5 x 1 4 x + 9 correct Explanation: To determine the inverse of f we first solve for x in y = 1 + 9 x 5 4 x . In this case x = 5 y 1 4 y + 9 . The inverse f 1 is now obtained by inter changing x, y . Thus y = f 1 ( x ) = 5 x 1 4 x + 9 . 005 10.0 points If a, b are the solutions of the exponential equation 3 x 2 = 9 1 2 x +6 , calculate the value of ab ....
View
Full
Document
 Spring '11
 Cathy

Click to edit the document details