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Practice Exam 2 - h ◦ f ◦ g x 5 For the following...

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Math 141 Monarres Practice Exam 2 October 4, 2006 1. For the following functions, f ( x ) and g ( x ), find ( f + g )( x ), ( f · g )( x ), f g ( x ), and give the domain of each new function. (a) f ( x ) = 4 - x 2 g ( x ) = x + 2 (b) f ( x ) = - 14 x 3 2 x > 3 g ( x ) = - 28 x 0 0 x > 0 (c) f ( x ) = x g ( x ) = x + 1 (d) f ( x ) = x 2 - 2 g ( x ) = x + 2 2. Consider the functions f ( x ) = 1 x + 2 g ( x ) = x - 2 h ( x ) = x 2 - 7 (a) Find ( g h )( x ) and tell me when it is defined. (b) Find ( f g h )( x ) and once again tell me when it is defined. 3. Remember that a function is just a relationship between sets. Consider the set of numbers A = { 1 , 2 , 3 , 4 , 5 } . Which of the following functions f : A A have inverses. (a) f ( x ) = 1 3 2 3 3 1 4 2 5 4 (b) f ( x ) = 1 5 2 3 3 1 4 2 5 4 (c) f ( x ) = 1 5 2 3 3 1 4 5 5 4 (d) f ( x ) = 1 5 2 4 3 3 4 2 5 1 1
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Math 141 Monarres Practice Exam 2 October 4, 2006 4. Let f ( x ) = x 2 + 2 x + 2 g ( x ) = x - 3 h ( x ) = 1 x Draw a graph 1 of the following functions: (a) ( f g )( x ) (b) ( g f )( x ) (c) ( h f )( x
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Unformatted text preview: h ◦ f ◦ g )( x ) 5. For the following statements, tell me whether they are true or false. (a) If the functions f ( x ) and g ( x ) are defined for all real numbers. Then ( f ◦ g )( x ) is also defined for all real numbers. (Is this true if the domains were the negative instead of all real numbers?) (b) A function is one-to-one provided that f ( x 1 ) 6 = f ( x 2 ), whenever x 1 6 = x 2 . (c) Let f ( x ) = b x c . Then 879.5 is in the range of f . (d) Let f ( x ) =-| x-2 | + 3. Then f ( x ) > 0 for all x. 6. “Understand” the following homework problems 2 : • 2.2: 38 • 2.3: 7 1 Remember to include intercepts, vertices,etc. .. 2 You should “understand” all of your homework not just these 2...
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