Roboguru

Pertanyaan

Jika f left parenthesis x right parenthesis equals square root of x squared minus 4 end root dan g left parenthesis x right parenthesis equals square root of x minus 2 end root, tentukanlah:

a. f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis (beserta domainnya)

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

 f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis equals square root of x squared minus 4 end root plus square root of x minus 2 end root dan D subscript f plus g end subscript equals open curly brackets x vertical line x greater or equal than 2 comma space x element of R close curly brackets

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah bold italic f bold left parenthesis bold italic x bold right parenthesis bold plus bold italic g bold left parenthesis bold italic x bold right parenthesis bold equals square root of bold x to the power of bold 2 bold minus bold 4 end root bold plus square root of bold x bold minus bold 2 end root dan Error converting from MathML to accessible text.
 

Ingat! 

D subscript f plus g end subscript equals D subscript f intersection D subscript g 

Perhatikan perhitungan berikut ini!

Diketahui f left parenthesis x right parenthesis equals square root of x squared minus 4 end root dan g left parenthesis x right parenthesis equals square root of x minus 2 end root
Diperoleh

f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis equals square root of x squared minus 4 end root plus square root of x minus 2 end root 

Domain f left parenthesis x right parenthesis equals square root of x squared minus 4 end root

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared minus 4 end cell greater or equal than 0 row cell open parentheses x plus 2 close parentheses open parentheses x minus 2 close parentheses end cell greater or equal than 0 row cell x minus 2 end cell equals cell 0 space space space atau space space x plus 2 equals 0 end cell row x equals cell 2 space space space space space space space space space space space space space space space space space space x equals negative 2 end cell end table 



Jadi, D subscript f equals open curly brackets x vertical line x less or equal than negative 2 space atau space x greater or equal than 2 comma space x space element of R close curly brackets

Domain g left parenthesis x right parenthesis equals square root of x minus 2 end root

table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 2 end cell greater or equal than 0 row x greater or equal than 2 end table 

Jadi, D subscript g equals open curly brackets x vertical line x greater or equal than 2 comma space x space element of R close curly brackets 

Domain dari f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis yaitu 

table attributes columnalign right center left columnspacing 0px end attributes row cell D subscript f plus g end subscript end cell equals cell D subscript f intersection D subscript g end cell row blank equals cell open curly brackets x vertical line x greater or equal than 2 comma space x element of R close curly brackets end cell end table  

Dengan demikian, f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis equals square root of x squared minus 4 end root plus square root of x minus 2 end root dan D subscript f plus g end subscript equals open curly brackets x vertical line x greater or equal than 2 comma space x element of R close curly brackets

94

3.6 (3 rating)

Pertanyaan serupa

Tentukan rumus fungsi (f+g)(x),(f⋅g)(x),(gf​)(x) dan daerah asalnya, jika diketahui f(x) dan g(x) berikut: f(x)=3x−6dang(x)=x−3​1​

22

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 Ruangguru

Produk Ruangguru

Produk Lainnya

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