Tentukan domain dan range setiap fungsi berikut. b. g(x)=3x−184x−20

Pertanyaan

Tentukan domain dan range setiap fungsi berikut.

b. $g(x)=\frac{4x-20}{3x-18}$

Pembahasan Soal:

Bentuk $g left parenthesis x right parenthesis equals fraction numerator 4 x minus 20 over denominator 3 x minus 18 end fraction$ terdefinisi untuk penyebut $not equal to 0$ , maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x minus 18 end cell not equal to 0 row cell 3 x end cell not equal to 18 row x not equal to cell 18 over 3 end cell row x not equal to 6 end table$

Sehingga, domain dari $y equals 4 x cubed minus 5$ adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 6 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank element of blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank R end table$

Menentukan range:

$table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis x right parenthesis end cell equals cell fraction numerator 4 x minus 20 over denominator 3 x minus 18 end fraction end cell row y equals cell fraction numerator 4 x minus 20 over denominator 3 x minus 18 end fraction end cell row cell y left parenthesis 3 x minus 18 right parenthesis end cell equals cell 4 x minus 20 end cell row cell 3 x y minus 18 y end cell equals cell 4 x minus 20 end cell row cell 3 x y minus 4 x end cell equals cell 18 y minus 20 end cell row cell x left parenthesis 3 y minus 4 right parenthesis end cell equals cell 18 y minus 20 end cell row x equals cell fraction numerator 18 y minus 20 over denominator 3 y minus 4 end fraction end cell end table$

Bentuk $table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 18 y minus 20 over denominator 3 y minus 4 end fraction end cell end table$ terdefinisi untuk penyebut $not equal to 0$ , maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell 3 y minus 4 end cell not equal to 0 row cell 3 y end cell not equal to 4 row y not equal to cell 4 over 3 end cell end table$

Sehingga, range dari $g left parenthesis x right parenthesis equals fraction numerator 4 x minus 20 over denominator 3 x minus 18 end fraction$ adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank y end table table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 4 over 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank y end table table attributes columnalign right center left columnspacing 0px end attributes row blank element of blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank R end table$ .

Jadi, domain fungsi $g left parenthesis x right parenthesis equals fraction numerator 4 x minus 20 over denominator 3 x minus 18 end fraction$ adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 6 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank element of blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank R end table$ dan rangenya adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank y end table table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 4 over 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank y end table table attributes columnalign right center left columnspacing 0px end attributes row blank element of blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank R end table$

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

I. Sutiawan

Mahasiswa/Alumni Universitas Pasundan

Terakhir diupdate 06 Oktober 2021