Roboguru

Pertanyaan

Diketahui fungsi begin mathsize 14px style f end style dan begin mathsize 14px style g end style didefinisikan sebagai pasangan berurutan sebagai berikut.

begin mathsize 14px style f equals open curly brackets open parentheses negative 2 comma space 1 close parentheses comma space open parentheses 0 comma space 3 close parentheses comma space open parentheses 2 comma space 5 close parentheses comma space open parentheses negative 1 comma space 7 close parentheses close curly brackets g equals open curly brackets open parentheses negative 2 comma space minus 3 close parentheses comma space open parentheses 0 comma space minus 2 close parentheses comma space open parentheses 2 comma space minus 1 close parentheses comma space open parentheses 4 comma space 0 close parentheses close curly brackets end style 

Tentukan:

c. begin mathsize 14px style open parentheses f cross times g close parentheses open parentheses x close parentheses end style 

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

begin mathsize 14px style left parenthesis f cross times g right parenthesis left parenthesis x right parenthesis equals 1 half x squared minus 1 half x minus 6 end style  

Pembahasan

Diketahui fungsi undefined dan undefined didefinisikan sebagai pasangan berurutan sebagai berikut.

begin mathsize 14px style f equals open curly brackets open parentheses negative 2 comma space 1 close parentheses comma space open parentheses 0 comma space 3 close parentheses comma space open parentheses 2 comma space 5 close parentheses comma space open parentheses negative 1 comma space 7 close parentheses close curly brackets g equals open curly brackets open parentheses negative 2 comma space minus 3 close parentheses comma space open parentheses 0 comma space minus 2 close parentheses comma space open parentheses 2 comma space minus 1 close parentheses comma space open parentheses 4 comma space 0 close parentheses close curly brackets end style

Langkah pertamanya adalah kita tentukan terlebih dahulu rumus fungsi undefined dan rumus fungsi undefined.

Misalkan undefined, maka:

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis negative 2 right parenthesis end cell equals cell a left parenthesis negative 2 right parenthesis plus b space space end cell row cell space 1 end cell equals cell negative 2 a plus b space.... space left parenthesis 1 right parenthesis space end cell row blank blank blank row cell space g left parenthesis 0 right parenthesis end cell equals cell a left parenthesis 0 right parenthesis plus b space space end cell row cell space 3 end cell equals cell b space............. space left parenthesis 2 right parenthesis end cell end table end style

Dari persamaan (1) dan (2) kita gunakan substitusi, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row 1 equals cell negative 2 a plus b space space end cell row 1 equals cell negative 2 a plus 3 space space end cell row cell 2 a end cell equals cell 3 minus 1 space end cell row cell space 2 a end cell equals cell 2 space space end cell row a equals 1 end table end style 

Makaundefined

Misalkan undefined, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis negative 2 right parenthesis end cell equals cell p left parenthesis negative 2 right parenthesis plus q space space end cell row cell negative 3 end cell equals cell negative 2 p plus q space.... space left parenthesis 3 right parenthesis space space end cell row blank blank blank row cell g left parenthesis 0 right parenthesis end cell equals cell p left parenthesis 0 right parenthesis plus q space space end cell row cell negative 2 end cell equals cell q space............. space left parenthesis 4 right parenthesis end cell end table end style 

Dari persamaan (3) dan (4) kita gunakan substitusi, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative 3 end cell equals cell negative 2 p plus q space space end cell row cell negative 3 end cell equals cell negative 2 p minus 2 space space end cell row cell 2 p end cell equals cell negative 2 plus 3 space space end cell row cell 2 p end cell equals cell 1 space space end cell row p equals cell 1 half end cell end table end style 

Maka undefined 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f cross times g right parenthesis left parenthesis x right parenthesis end cell equals cell f left parenthesis left parenthesis x right parenthesis cross times g left parenthesis x right parenthesis end cell row blank equals cell left parenthesis x plus 3 right parenthesis left parenthesis 1 half x minus 2 right parenthesis end cell row blank equals cell 1 half x squared minus 2 x plus 3 over 2 x minus 6 end cell row blank equals cell 1 half x squared minus 1 half x minus 6 end cell end table end style 

Jadi, begin mathsize 14px style left parenthesis f cross times g right parenthesis left parenthesis x right parenthesis equals 1 half x squared minus 1 half x minus 6 end style  

25

0.0 (0 rating)

Pertanyaan serupa

Diketahui fungsi f(x)=2x+3 dan g(x)=x−6, maka (f⋅g)(x) adalah ...

25

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