Q3SOL - MAP 103 Proficiency Algebra Quiz#3 Fall 2009...

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Unformatted text preview: MAP 103: Proficiency Algebra, Quiz #3, Fall 2009 SOLUTIONS 1. Consider a relation R = { (- 1 , 1) , (0 , 1) , (2 , 4) , (5 , 5) , (5 , 6) , (6 , 2) , (10 , 8) } . (a) State the domain and range of R. Sol. The domain is D = {- 1 , , 2 , 5 , 10 } and the range is R = { 1 , 2 , 4 , 5 , 8 } . (b) Is the relation given by R a function? Explain. Sol. The relation R is not a function since it fails the vertical line test at points (5 , 5) and (5 , 6) . (c) Is the relation given by R a 1- 1 function? Sol. By (b) it is not 1- 1 . (d) Is the relation given by R an onto function? Sol. By (b) it is not onto. 2. Consider two functions f ( x ) = √ 1- x and g ( x ) = x 2- 1 . (a) Find ( f + g )(2) . Sol. Since √ 1- x > 0 only when x 6 1 , we cannot evaluate it at x = 2 . Thus, f (2)+ g (2) is not defined when x = 2 . (b) Determine the domain of ( f + g )( x ) . Sol. Since √ 1- x > 0 only when x 6 1 , while g ( x ) is well-defined for all real x, the domain of f ( x ) + g ( x ) is D = { x | x 6 1...
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Q3SOL - MAP 103 Proficiency Algebra Quiz#3 Fall 2009...

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