Roboguru

Diketahui fungsi  dan . Tentukan fungsi-fungsi berikut dan tentukan pula daerah asalnya.

Pertanyaan

Diketahui fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals square root of x squared minus 4 end root end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals square root of x minus 2 end root end style. Tentukan fungsi-fungsi berikut dan tentukan pula daerah asalnya.

begin mathsize 14px style left parenthesis f plus g right parenthesis left parenthesis x right parenthesis end style 

Pembahasan Soal:

Diketahui fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals square root of x squared minus 4 end root end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals square root of x minus 2 end root end style. Selanjutnya

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f plus g close parentheses left parenthesis x right parenthesis end cell equals cell f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis end cell row blank equals cell square root of x squared minus 4 end root plus square root of x minus 2 end root end cell end table  

Domain open parentheses f plus g close parentheses left parenthesis x right parenthesis space adalah space straight D subscript straight f large intersection straight D subscript straight g.

Domain f left parenthesis x right parenthesis space atau space D subscript f colon

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

Didapat : x less or equal than negative 2 space atau space x greater or equal than 2 space... space left parenthesis 1 right parenthesis

Domain g left parenthesis x right parenthesis space atau space D subscript g colon

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 cell 2 space... space left parenthesis 2 right parenthesis end cell end table

Irisan (1) dan (2):

Didapat domain open parentheses f plus g close parentheses left parenthesis x right parenthesis colon space open curly brackets x element of R colon space x greater or equal than 2 close curly brackets

Jadi hasil operasi open parentheses f plus g close parentheses 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 domain open parentheses f plus g close parentheses left parenthesis x right parenthesis colon space open curly brackets x element of R colon space x greater or equal than 2 close curly brackets

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 19 Mei 2021

Ruangguru

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

Ikuti Kami

©2021 Ruangguru. All Rights Reserved