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Review 3-solutions

# Review 3-solutions - wtm369 Review 3 Helleloid(58250 This...

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wtm369 – Review 3 – Helleloid – (58250) 1 This print-out should have 19 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Find the value of x when x = 8 log 4 parenleftBig 1 16 parenrightBig 7 log 3 27 without using a calculator. 1. x = 34 2. x = 37 3. x = 33 4. x = 33 5. x = 37 correct Explanation: By properties of logs, log 4 parenleftBig 1 16 parenrightBig = log 4 parenleftBig 1 (4) 2 parenrightBig = 2 , while log 3 27 = log 3 (3) 3 = 3 . Consequently, x = 21 16 = 37 . 002 10.0 points Simplify the expression f ( x ) = 8 2(log 8 e )ln x as much as possible. 1. f ( x ) = 2 x 2. f ( x ) = x 8 3. f ( x ) = e 17 4. f ( x ) = x 16 5. f ( x ) = x 2 correct Explanation: By the property of inverse functions, 8 log 8 y = y, e ln y = y . Consequently, f ( x ) = 8 2(log 8 e )ln x = (8 log 8 e ) 2ln x = e ln x 2 = x 2 . 003 10.0 points Five functions are defined by the table x f ( x ) g ( x ) h ( x ) F ( x ) G ( x ) 1 2 3 4 5 6 9 6 2 7 8 1 2 8 4 6 9 7 7 2 8 6 4 3 3 8 1 6 2 9 2 4 9 8 2 7 Which of these functions is not 1-1? 1. h ( x ) 2. G ( x ) correct 3. g ( x ) 4. F ( x ) 5. f ( x ) Explanation:

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wtm369 – Review 3 – Helleloid – (58250) 2 The function G ( x ) is not 1-1 since G (1) = G (5) . keywords: inverse function, function values 1-1 function 004 10.0 points If f is the function defined by f ( x ) = 3 x 2 ( x 0) , determine the inverse function, f 1 , of f . 1. f 1 ( x ) = radicalbigg x 3 , ( x 0) correct 2. f 1 ( x ) = radicalbigg x 3 , ( x 0) 3. f 1 ( x ) = radicalbigg x 3 , ( x 0) 4. f 1 ( x ) = radicalbigg x 3 , ( x 0) 5. f 1 ( x ) = radicalbigg x 3 , ( x 0) Explanation: The function defined by f ( x ) = 3 x 2 is one- to-one so long as x is restricted to x 0; hence the inverse function, f 1 , exists. Now 3 x 2 = y, ( y > 0) = x = ± radicalbigg y 3 . To determine f 1 we interchange the roles of x and y . But the original function f is defined only for x 0. Consequently, f 1 ( x ) = radicalbigg x 3 , ( x 0) . 005 10.0 points On ( 1 , 1) the function f ( x ) = 4 + x 2 + tan parenleftBig πx 2 parenrightBig has an inverse g . Find the value of g (4). (Hint: find the value of f (0)). 1. g (4) = 2 π correct 2. g (4) = π 2 3. g (4) = 4 π 4. g (4) = 1 5. g (4) = π 4 Explanation: By definition of inverse function: f ( g ( x )) = x , g ( f ( x )) = x . Applying the Chain Rule to the first of these equations, we see that f ( g ( x )) g ( x ) = 1 , in which case g ( x ) = 1 f ( g ( x )) . Thus to find the value of g (4) we need to know the value of g (4) as well as f ( x ). Now f ( x ) = 2 x + π 2 sec 2 parenleftBig πx 2 parenrightBig .
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Review 3-solutions - wtm369 Review 3 Helleloid(58250 This...

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