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HW3-solutions

# HW3-solutions - wei(jw35975 HW3 milburn(54685 This...

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wei (jw35975) – HW3 – milburn – (54685) 1 This print-out should have 23 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points ±ive Functions are defned by the table x f ( x ) g ( x ) h ( x ) F ( x ) G ( x ) 1 2 3 4 5 6 2 9 3 8 2 7 9 7 8 7 3 6 6 5 2 9 8 2 3 5 2 7 4 6 2 6 3 9 3 8 Which oF these Functions is one-to-one? 1. G ( x ) 2. h ( x ) 3. f ( x ) 4. g ( x ) 5. F ( x ) correct Explanation: The Function y = F ( x ) is the only one-to- one Function since f (1) = f (5) , g (2) = g (4) , h (3) = h (6) , G (3) = G (5) . keywords: one-to-one, Function value, 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 3. 4 8 4 8 4 8 4 8

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wei (jw35975) – HW3 – milburn – (54685) 2 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 Explanation: The graph of f - 1 ( x ) is obtained by reFect- ing the graph of f over the line y = x : 4 8 4 8 4 8 4 8 003 10.0 points ±ind the inverse function, f - 1 , for f when f ( x ) = r 36 x 2 , 0 x 6 . 1. f - 1 ( x ) = r x 2 36 , 6 x 6 2. f - 1 ( x ) = r 36 x 2 , 0 x 6 correct 3. f - 1 ( x ) = r 36 x 2 , 6 x 6 4. inverse doesn’t exist 5. f - 1 ( x ) = 1 36 x 2 , 0 x < 6 Explanation: As the graph 6 6 f = f - 1 of f shows, the given f is 1-1 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 = r 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 ) = r 36 x 2 , 0 x 6 . 004 10.0 points
wei (jw35975) – HW3 – milburn – (54685) 3 Rewrite 5 log 3 x = 3 in equivalent exponential form. 1. x 5 = 1 27 correct 2. x 3 = 10 3. x 5 = 27 4. x 3 = 1 27 5. x 5 = 10 Explanation: By exponentiation to the base 3, 3 5 log 3 x = 1 27 . But 3 5 log 3 x = 3 log 3 x 5 = x 5 . Hence the exponential form of the given equa- tion is x 5 = 1 27 . keywords: LogFunc, LogFuncExam, 005 10.0 points Find the value of x when x = 6 log 3 p 1 27 P 9 log 4 64 without using a calculator. 1. x = 45 correct 2. x = 45 3. x = 41 4. x = 41 5. x = 42 Explanation: By properties of logs, log 3 p 1 27 P = log 3 p 1 (3) 3 P = 3 , while log 4 64 = log 4 (4) 3 = 3 . Consequently, x = 27 18 = 45 . 006 10.0 points Find the value of x when x = 4 log 6 p 4 6 3 P 6 log 3 p 3 3 4 P . 1. x = 31 6 2. x = 21 4 3. x = 5 correct 4. x = 61 12 5. x = 59 12 Explanation: Since r log a z = log a z r , log a a = 1 , we see that log 6 p 4 6 3 P = 3 4 , while log 3 p 3 3 4 P = 4 3 .

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wei (jw35975) – HW3 – milburn – (54685) 4 Consequently, x = 5 .
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HW3-solutions - wei(jw35975 HW3 milburn(54685 This...

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