Roboguru

Pertanyaan

Diketahui rumus fungsi begin mathsize 14px style g left parenthesis x right parenthesis equals square root of x minus 3 end root end style dan begin mathsize 14px style left parenthesis g cross times h right parenthesis left parenthesis x right parenthesis equals square root of x squared minus x minus 6 end root end style. Tentukan rumus fungsi begin mathsize 14px style h end style beserta domainnya.

  1. ...space 

  2. ...space 

S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

domain fungsi begin mathsize 14px style h end style adalah begin mathsize 14px style D subscript h equals left curly bracket x vertical line x greater or equal than negative 2 comma x element of straight real numbers right curly bracket end style.

Pembahasan

Diketahui dua fungsi yaitu begin mathsize 14px style g left parenthesis x right parenthesis equals square root of x minus 3 end root end style dan begin mathsize 14px style left parenthesis g cross times h right parenthesis left parenthesis x right parenthesis equals square root of x squared minus x minus 6 end root end style.
Sehingga, didapat:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g cross times h close parentheses open parentheses x close parentheses end cell equals cell square root of x squared minus x minus 6 end root blank end cell row cell g open parentheses x close parentheses cross times h open parentheses x close parentheses end cell equals cell square root of open parentheses x minus 3 close parentheses open parentheses x plus 2 close parentheses end root blank end cell row cell square root of x minus 3 end root cross times h open parentheses x close parentheses end cell equals cell square root of x minus 3 end root cross times square root of x plus 2 end root blank end cell row cell h open parentheses x close parentheses end cell equals cell fraction numerator square root of x minus 3 end root cross times square root of x plus 2 end root over denominator square root of x minus 3 end root end fraction blank end cell row cell h open parentheses x close parentheses end cell equals cell square root of x blank plus blank 2 end root end cell end table end style 

Mencari domain:
Fungsi begin mathsize 14px style h end style terdefinisi pada begin mathsize 14px style x end style real, jika:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x plus 2 end cell greater or equal than cell 0 space end cell row x greater or equal than cell negative 2 end cell end table end style 

Jadi, domain fungsi begin mathsize 14px style h end style adalah begin mathsize 14px style D subscript h equals left curly bracket x vertical line x greater or equal than negative 2 comma x element of straight real numbers right curly bracket end style.

38

5.0 (1 rating)

Pertanyaan serupa

Diketahui fungsi f(x)=x+3 dan g(x)=x−9. Tentukanlah fungsi-fungsi berikut dan tentukan pula daerah asalnya. (f×g)

28

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