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

Question

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

Makenna Lin · Accepted Answer

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  +  4Let   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

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)

Answered question

Answer & Explanation

New Questions in Algebra I