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: silva (jrs4378) – Hw 13 – gualdani – (56455) 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. A only 2. none of them 3. A and C only 4. all of them 5. B and C only 6. A and B only correct 7. B only 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 2. 4 8 4 8 4 8 4 8 silva (jrs4378) – Hw 13 – gualdani – (56455) 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 correct 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 36 x 2 , ≤ x ≤ 6 . 1. inverse doesn’t exist 2. f − 1 ( x ) = radicalbig 36 x 2 , 6 ≤ x ≤ 6 3. f − 1 ( x ) = radicalbig x 2 36 , 6 ≤ x ≤ 6 4. f − 1 ( x ) = radicalbig 36 x 2 , ≤ x ≤ 6 correct 5. f − 1 ( x ) = 1 √ 36 x 2 , ≤ x < 6 Explanation: As the graph 6 6 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 36 y 2 for y . Squaring both sides and simplifying we obtain x 2 = 36 y 2 , i . e ., y 2 = 36 x 2 . Consequently, f − 1 ( x ) = radicalbig 36 y 2 , ≤ x ≤ 6 . 004 10.0 points silva (jrs4378) – Hw 13 – gualdani – (56455) 3 Find the inverse of f ( x ) = 1 + 3 x 6 5 x . 1. f − 1 ( x ) = 6 x 1 3 x + 5 2. f − 1 ( x ) = 6 x + 1 5 x + 3 3. f − 1 ( x ) = 6 x + 1 3 x + 5 4. f − 1 ( x ) = 6 x 1 5 x + 3 correct 5. f − 1 ( x ) = 3 x 1 5 x + 6 Explanation: To determine the inverse of f we first solve for x in y = 1 + 3 x 6 5 x . In this case x = 6 y 1 5 y + 3 . The inverse f − 1 is now obtained by inter changing x, y . Thus y = f − 1 ( x ) = 6 x 1 5 x + 3 . 005 10.0 points If a, b are the solutions of the exponential equation 5 x 2 = 25 5 x − 12 , calculate the value of ab ....
View
Full
Document
This note was uploaded on 08/29/2010 for the course M 46455 taught by Professor Gualdani during the Spring '10 term at University of Texas at Austin.
 Spring '10
 Gualdani

Click to edit the document details