Roboguru

Pertanyaan

Diketahui fungsi begin mathsize 14px style f colon space straight real numbers rightwards arrow straight real numbers end style dan begin mathsize 14px style g colon space straight real numbers rightwards arrow straight real numbers end style dengan begin mathsize 14px style f left parenthesis x right parenthesis equals 3 x plus 5 end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals fraction numerator 1 over denominator x plus 2 end fraction end style. Tentukan:

a. begin mathsize 14px style f ring operator g end style 

A. Acfreelance

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank f end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank ring operator end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank g end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 5 x plus 13 over denominator x plus 2 end fraction end cell end table end style.

Pembahasan

Fungsi komposisi merupakan penggabungan operasi dua jenis fungsi begin mathsize 14px style f left parenthesis x right parenthesis end style dan size 14px g size 14px left parenthesis size 14px x size 14px right parenthesis sehingga menghasilkan sebuah fungsi baru. Operasi fungsi komposisi biasa dilambangkan dengan "begin mathsize 14px style ring operator end style" dan dibaca komposisi atau bundaran. Fungsi baru yang dapat terbentuk dari begin mathsize 14px style f left parenthesis x right parenthesis end style dan size 14px g size 14px left parenthesis size 14px x size 14px right parenthesis adalah:

  1. begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses end style artinya size 14px g dimasukkan ke size 14px f 
  2. begin mathsize 14px style open parentheses g ring operator f close parentheses open parentheses x close parentheses end style artinya size 14px f dimasukkan ke size 14px g

Diketahui fungsi begin mathsize 14px style f colon space straight real numbers rightwards arrow straight real numbers end style dan begin mathsize 14px style g colon space straight real numbers rightwards arrow straight real numbers end style dengan begin mathsize 14px style f left parenthesis x right parenthesis equals 3 x plus 5 end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals fraction numerator 1 over denominator x plus 2 end fraction end style, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f ring operator g end cell equals cell open parentheses f ring operator g close parentheses left parenthesis x right parenthesis end cell row blank equals cell f open parentheses g open parentheses x close parentheses close parentheses end cell row blank equals cell f open parentheses fraction numerator 1 over denominator x plus 2 end fraction close parentheses end cell row blank equals cell 3 open parentheses fraction numerator 1 over denominator x plus 2 end fraction close parentheses plus 5 end cell row blank equals cell fraction numerator 3 over denominator x plus 2 end fraction plus 5 end cell row blank equals cell fraction numerator 3 plus 5 open parentheses x plus 2 close parentheses over denominator x plus 2 end fraction end cell row blank equals cell fraction numerator 3 plus 5 x plus 10 over denominator x plus 2 end fraction end cell row blank equals cell fraction numerator 5 x plus 13 over denominator x plus 2 end fraction end cell end table end style 

Jadi, begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank f end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank ring operator end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank g end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 5 x plus 13 over denominator x plus 2 end fraction end cell end table end style.

16

0.0 (0 rating)

Pertanyaan serupa

Jika f(x)=x−5 dan g(x)=x2−1, maka (f∘g)(x)=...

34

5.0

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