Tentukan domain dan range setiap fungsi berikut. c. f(x)=x3−5x3+3​

Pertanyaan

Tentukan domain dan range setiap fungsi berikut.

c. f left parenthesis x right parenthesis equals fraction numerator x cubed plus 3 over denominator x cubed minus 5 end fraction 

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

domain fungsi f left parenthesis x right parenthesis equals fraction numerator x cubed plus 3 over denominator x cubed minus 5 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 cell cube root of 5 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 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 y table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table 1 table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell comma space end cell 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

Bentuk f left parenthesis x right parenthesis equals fraction numerator x cubed plus 3 over denominator x cubed minus 5 end fraction terdefinisi untuk penyebut not equal to 0, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell x cubed minus 5 end cell not equal to 0 row cell x cubed end cell not equal to 5 row x not equal to cell cube root of 5 end cell end table 

Sehingga, domain dari f left parenthesis x right parenthesis equals fraction numerator x cubed plus 3 over denominator x cubed minus 5 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 cell cube root of 5 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 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 y equals cell fraction numerator x cubed plus 3 over denominator x cubed minus 5 end fraction end cell row cell y left parenthesis x cubed minus 5 right parenthesis end cell equals cell x cubed plus 3 end cell row cell x cubed y minus 5 y end cell equals cell x cubed plus 3 end cell row cell x cubed y minus x cubed end cell equals cell 5 y plus 3 end cell row cell x cubed left parenthesis y minus 1 right parenthesis end cell equals cell 5 y plus 3 end cell row cell x cubed end cell equals cell fraction numerator 5 y plus 3 over denominator y minus 1 end fraction end cell row x equals cell cube root of fraction numerator 5 y plus 3 over denominator y minus 1 end fraction end root end cell end table 

Bentuk x equals cube root of fraction numerator 5 y plus 3 over denominator y minus 1 end fraction end root terdefinisi untuk penyebut not equal to 0, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell cube root of y minus 1 end root end cell not equal to 0 row cell y minus 1 end cell not equal to 0 row y not equal to 1 end table 

Sehingga, range dari f left parenthesis x right parenthesis equals fraction numerator x cubed plus 3 over denominator x cubed minus 5 end fraction adalah y table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table 1 table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell comma space end cell 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 f left parenthesis x right parenthesis equals fraction numerator x cubed plus 3 over denominator x cubed minus 5 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 cell cube root of 5 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 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 y table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table 1 table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell comma space end cell 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 

53

5.0 (1 rating)

Pertanyaan serupa

Carilah interval D terbesar pada rumus f(x)=x2 agar fungsi tersebut merupakan fungsi one-one

55

0.0

Jawaban terverifikasi

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

Fitur Roboguru

Topik Roboguru

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia