The one-to-one functions g and h are defined as follows. g={(-6,-5),(1,5),(4,8),(5,-3)} h(x)=3x+4 Find the following. g^(-1)(5)=? h^(-1)(x)=? (h * h^(-1))(7)

Marisol Rivers 2022-07-19 Answered
The one-to-one functions g and h are defined as follows.
g = { ( 6 , 5 ) , ( 1 , 5 ) , ( 4 , 8 ) , ( 5 , 3 ) }
h(x)=3x+4
Find the following.
g 1 ( 5 ) = ? h 1 ( x ) = ? ( h h 1 ) ( 7 )
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Answers (1)

Makenna Lin
Answered 2022-07-20 Author has 16 answers
g = { ( 6 , 5 ) , ( 1 , 5 ) , ( 4 , 8 ) , ( 5 , 3 ) } h ( x ) = 3 x + 4 g 1 = { ( 5 , 6 ) , ( 5 , 1 ) , ( 8 , 4 ) , ( 3 , 5 ) } g 1 ( 5 ) = { 1 }
h ( x ) = 3 x + 4
Let h ( x ) = y x = h 1 ( y ) 3 x + 4 = y 3 x = y 4 x = y 4 3 h 1 ( y ) = y 4 3 h 1 ( x ) = x 4 3       ( swap x and y )
( h h 1 ) ( 7 ) = h [ h 1 ( 7 ) ] = h [ 7 4 3 ] = h [ 3 3 ] = h ( 1 ) = 3 ( 1 ) + 4 = 3 + 4 ( h h 1 ) ( 7 ) = 7

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