01%20-%20Sets,%20Relations%20and%20Functions

01%20-%20Sets,%20Relations%20and%20Functions - 01 - SETS,...

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01 - SETS, RELATIONS AND FUNCTIONS Page 1 ( Answers at the end of all questions ) ( 1 ) Let R = { ( 3, 3 ) ( 6, 6 ) ( ( 9, 9 ) ( 12, 12 ), ( 6, 12 ) ( 3, 9 ) ( 3, 12 ), ( 3, 6 ) } be a relation on the set A = { 3, 6, 9, 12 }. The relation is ( a ) reflexive and transitive ( b ) reflexive only ( c ) an equivalence relation ( d ) reflexive and symmetric only [ AIEEE 2005 ] ( 2 ) Let f : ( - 1, 1 ) B be a function defined by f ( x ) = 2 1 x 1 2x tan - - , then f is both one-one and onto when B is the interval ( a ) π 2 , 0 ( b ) π 2 , 0 ( c ) π π 2 , 2 - ( d ) π π 2 , 2 - [ AIEEE 2005 ] ( 3 ) If a real valued function f ( x ) satisfies the functional equation f ( x - y ) = f ( x ) f ( y ) - f ( a - x ) f ( a + y ), where ‘a’ is a given constant and f ( 0 ) = 1, then f ( 2a - x ) is equal to ( a ) - f ( x ) ( b ) f ( x ) ( c ) f ( a ) + f ( a - x ) ( d ) f ( - x ) [ AIEEE 2005 ] ( 4 ) Let R = { ( 1, 3 ), ( 4, 2 ), ( 2, 4 ), ( 2, 3 ), ( 3, 1 ) } be a relation on the set A = { 1, 2, 3, 4 }. The relation R is ( a ) a function ( b ) transitive ( c ) not symmetric ( d ) reflexive [ AIEEE 2004 ] ( 5 ) The range of the function f ( x ) = 3 x x 7 P - - is ( a ) { 1, 2, 3 } ( b ) { 1, 2, 3, 4, 5, 6 } ( c ) { 1, 2, 3, 4 } ( d ) { 1, 2, 3, 4, 5 } [ AIEEE 2004 ] ( 6 ) If f : R S, defined by f( x ) = sin x - 3 cos x + 1 is onto, then the interval of S is ( a ) [ 0, 3 ] ( b ) [ - 1, 1 ] ( c ) [ 0, 1 ] ( d ) [ - 1, 3 ] [ AIEEE 2004 ] ( 7 ) The graph of the function f ( x ) is symmetrical about the line x =2, then ( a ) f ( x + 2 ) = f ( x - 2 ) ( b ) f ( 2 + x ) = f ( 2 - x ) ( c ) f ( x ) = f ( - x ) ( d ) f ( x ) = - f ( - x ) [ AIEEE 2004 ]
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01 - SETS, RELATIONS AND FUNCTIONS Page 2 ( Answers at the end of all questions ) ( 8 ) The domain of the function f ( x ) = 2 1 x 9 ) 3 x ( sin - - - is ( a ) [ 2, 3 ] ( b ) [ 2, 3 ) ( c ) [ 1, 2 ] ( d ) [ 1, 2 ) [ AIEEE 2004 ] ( 9 ) If f : { 1, 2, 3, …. } { 0, ± 1, ± 2, ….. } is defined by f ( x ) = odd is x if , 2 ) 1 x ( even is x if , 2 x - - then value of f - 1 ( - 100 ) is ( a ) 100 ( b ) 199 ( c ) 200 ( d )
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This note was uploaded on 11/28/2011 for the course PHYSICS 300 taught by Professor Smith during the Spring '06 term at ITT Tech Flint.

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01%20-%20Sets,%20Relations%20and%20Functions - 01 - SETS,...

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