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: chapman (jtc984) HW03 meth (54865) 1 This printout should have 27 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 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 6. 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 : chapman (jtc984) HW03 meth (54865) 2 4 8 4 8 4 8 4 8 002 10.0 points Find the inverse function, f 1 , of f ( x ) = 4 x 8 x 2 + 1 . 1. f 1 ( x ) = 16 + 8 x 2 x 2. f 1 ( x ) = 8 16 x 2 3. f 1 ( x ) = 16 x 2 8 4. f 1 ( x ) = 16 8 x 2 8 x 5. f 1 ( x ) = x 16 + 8 x 2 6. f 1 ( x ) = x 16 8 x 2 correct Explanation: The graph of f ( x ) = 4 x 8 x 2 + 1 , is shown as a continuous line in f f 1 Since this graph passes the horizontal line test, f will have an inverse, f 1 , whose graph is shown as a dotted line. Algebraically, this inverse function is defined by y = f 1 ( x ) where x = 4 y radicalbig 8 y 2 + 1 . Solving for y we see that 16 y 2 = x 2 ( 8 y 2 + 1 ) = 8 x 2 y 2 + x 2 , i.e. , y 2 ( 16 8 x 2 ) = x 2 . Thus y = x 16 8 x 2 , 4 8 < x < 4 8 , and so f 1 ( x ) = x 16 8 x 2 , 4 8 < x < 4 8 . 003 10.0 points Use properties of logs to simplify the ex pression log a 32 + 3 5 log a 10 3 5 log a 5 + log a 1 2 13 5 as much as possible. 1. log a 128 2. 8 3. log a 2 7 4. log a 8 correct chapman (jtc984) HW03 meth (54865) 3 5. log a 32 Explanation: By properties of logs the given expression can be rewritten as log a braceleftBig 2 5 10 3 5 5 3 5 2 2 2 3 5 bracerightBig = log a 8 . 004 10.0 points Solve for x when e 3 x = 1 32 . 1. x = 15 ln 2 2. x = 15 ln5 3. x = 5 3 ln 2 correct 4. x = 5 ln5 5. x = 5 ln 5 6. x = 5 3 ln2 Explanation: Taking logs of both sides we see that ln( e 3 x ) = ln 1 32 . Thus ln 1 32 = 3 x ln e = 3 x . Now ln 1 32 = ln 2 5 = 5 ln2 . Consequently, x = 5 3 ln 2 . keywords: LogFunc, LogFuncExam, 005 10.0 points Which of the following statements are true for all positive x, y , and a, a negationslash = 1? A. log a x log a y = log a ( x/y ) , B. log a x + log a y = log a xy , C. 2 log a x = (log a x ) 2 . 1. A and B only correct 2. C only 3. A only 4. all of them 5. A and C only 6. none of them 7. B and C only 8. B only Explanation: A. TRUE: by properties of logs....
View Full
Document
 Fall '08
 schultz
 Calculus

Click to edit the document details