HW03-solutions

HW03-solutions - chapman(jtc984 HW03 meth(54865 This...

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chapman (jtc984) – HW03 – meth – (54865) 1 This print-out should have 27 questions. Multiple-choice questions may continue on the next column or page – fnd 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 re±ect- ing the graph oF f over the line y = x :
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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 de±ned by y = f 1 ( x ) where x = 4 y r 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
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chapman (jtc984) – HW03 – meth – (54865) 3 5. log a 32 Explanation: By properties of logs the given expression can be rewritten as log a b 2 5 · 10 3 5 5 3 5 · 2 2 · 2 3 5 B = log a 8 . 004 10.0 points Solve for x when e 3 x = 1 32 . 1. x = 15 ln 2 2. x = 15 ln 5 3. x = 5 3 ln 2 correct 4. x = 5 ln 5 5. x = 5 ln 5 6. x = 5 3 ln 2 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 ln 2 . 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 n = 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. B. TRUE: by properties of logs. C. FALSE: by properties of logs log a ( x r ) = r log a x , so 2 log a x = log a ( x 2 ) . keywords: TrueFalse, T/F, properties of logs, logs, PlaceUT, 006 10.0 points If f is a one-to-one function such that f (6) = 1, what is the value of f 1 (1)? 1. f 1 (1) = 8 2. not enough information given
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chapman (jtc984) – HW03 – meth – (54865) 4 3. f 1 (1) = 10 4. f 1 (1) = 7 5. f 1 (1) = 6 correct 6. f 1 (1) = 11 Explanation: Since f (6) = 1 and f is one-to-one, the inverse, f 1 , of f exists and f 1 ( f ( x )) = f ( f 1 ( x )) = x .
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HW03-solutions - chapman(jtc984 HW03 meth(54865 This...

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