Test 2 Solutions

# 4 points each for this problem let 2 2 x x f 6 x x g

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(4 points each) For this problem, let 2 2 ) ( x x f = , 6 ) ( + - = x x g , and 3 4 ) ( x x h - = a. What is ) )( ( x f g ? 6 ) 2 ( ) 2 ( )) ( ( ) )( ( 2 2 + - = = = x x g x f g x f g b. What is ) )( ( x g h ? 3 ) 6 ( 4 ) 6 ( )) ( ( ) )( ( + - - = + - = = x x h x g h x g h

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Test 2 Name: ________________________ Math 115 – 001 September 11, 2008 9. (8 points each) Find all roots of the following polynomials using any method. a. 6 ) ( 3 - - = x x x f 0 3 2 1 6 4 2 6 1 0 1 2 - - 2 is a root; ) 3 2 )( 2 ( 6 ) ( 2 3 + + - = - - = x x x x x x f 3 2 2 + + x x = 0 2 ) 3 )( 1 ( 4 2 2 2 - ± - = x is not a real number; 2 is the only root. b. 24 ) ( 16 ) ( 2 ) ( 2 2 2 + + - + = x x x x x f Let y = x x + 2 ) 2 )( 6 ( 0 12 8 0 24 16 2 0 2 2 - - = + - = + - = y y y y y y y = 6 or y = 2 2 , 3 6 0 6 2 2 - = - + = + = = x x x x x y 1 , 2 2 0 2 2 2 - = - + = + = = x x x x x y x = –3, –2, 1, 2 10. (8 points) Write the inverse function of 3 ) ( 3 + = x x f and write the compositions ) )( ( 1 x f f - and ) )( ( 1 x f f - to verify that you have the correct inverse. 3 1 3 ) ( - = - x x f x x x x f x f f x f f = = - + = + = = - - - 3 3 3 3 3 1 1 1 3 ) 3 ( ) 3 ( )) ( ( ) )( ( ( 29 x x x x f x f f x f f = + - = + - = - = = - - 3 ) 3 ( 3 3 ) 3 ( )) ( ( ) )( ( 3 3 3 1 1 11. (4 points each) Describe the end behavior of a. 14 8 6 58 2 ) ( 9 10 15 16 + - + - + - = x x x x x x f As x goes to infinity, f ( x ) goes to minus infinity As x goes to minus infinity, f ( x
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• Fall '09
• Ms.Park
• Math, Inverse function, Polynomial long division, J B N F H Q P M O E

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