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Tentukan domain dan range setiap fungsi berikut. d. g ( x ) = 3 x 3 + 24 2 x 3 − 7 ​

Tentukan domain dan range setiap fungsi berikut.

d. 

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I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

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domain fungsi adalah dan rangenya adalah

domain fungsi g left parenthesis x right parenthesis equals fraction numerator 2 x cubed minus 7 over denominator 3 x cubed plus 24 end fraction adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table comma space x element of R dan rangenya adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank y end table table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 over 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank y end table table attributes columnalign right center left columnspacing 0px end attributes row blank element of blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank R end table 

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Pembahasan

Bentuk terdefinisi untuk penyebut , maka: Sehingga, domain dari adalah . Menentukan range: Bentuk terdefinisi untuk penyebut , maka: Sehingga, range dari adalah . Jadi, domain fungsi adalah dan rangenya adalah

Bentuk g left parenthesis x right parenthesis equals fraction numerator 2 x cubed minus 7 over denominator 3 x cubed plus 24 end fraction terdefinisi untuk penyebut not equal to 0, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x cubed plus 24 end cell not equal to 0 row cell 3 x cubed end cell not equal to cell negative 24 end cell row cell x cubed end cell not equal to cell fraction numerator negative 24 over denominator 3 end fraction end cell row cell x cubed end cell not equal to cell negative 8 end cell row x not equal to cell cube root of negative 8 end root end cell row x not equal to cell negative 2 end cell end table 

Sehingga, domain dari g left parenthesis x right parenthesis equals fraction numerator 2 x cubed minus 7 over denominator 3 x cubed plus 24 end fraction adalah  table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table comma space x element of R.

Menentukan range:

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell fraction numerator 2 x cubed minus 7 over denominator 3 x cubed plus 24 end fraction end cell row cell y left parenthesis 3 x cubed plus 24 right parenthesis end cell equals cell 2 x cubed minus 7 end cell row cell 3 x cubed y plus 24 y end cell equals cell 2 x cubed minus 7 end cell row cell 3 x cubed y minus 2 x cubed end cell equals cell negative 24 y minus 7 end cell row cell x cubed left parenthesis 3 y minus 2 right parenthesis end cell equals cell negative 24 y minus 7 end cell row cell x cubed end cell equals cell fraction numerator negative 24 y minus 7 over denominator 3 y minus 2 end fraction end cell row x equals cell cube root of fraction numerator negative 24 y minus 7 over denominator 3 y minus 2 end fraction end root end cell end table 

Bentuk table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell cube root of fraction numerator negative 24 y minus 7 over denominator 3 y minus 2 end fraction end root end cell end table terdefinisi untuk penyebut not equal to 0, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell cube root of 3 y minus 2 end root end cell not equal to 0 row cell 3 y minus 2 end cell not equal to 0 row cell 3 y end cell not equal to 2 row y not equal to cell 2 over 3 end cell end table 

Sehingga, range dari g left parenthesis x right parenthesis equals fraction numerator 2 x cubed minus 7 over denominator 3 x cubed plus 24 end fraction adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank y end table table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 over 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank y end table table attributes columnalign right center left columnspacing 0px end attributes row blank element of blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank R end table.

Jadi, domain fungsi g left parenthesis x right parenthesis equals fraction numerator 2 x cubed minus 7 over denominator 3 x cubed plus 24 end fraction adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table comma space x element of R dan rangenya adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank y end table table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 over 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank y end table table attributes columnalign right center left columnspacing 0px end attributes row blank element of blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank R end table 

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