Iklan

Iklan

Pertanyaan

Jika f ( x ) = x + 1 dan g ( x ) = x + 1 2 x ​ , maka ( g − 1 ∘ f − 1 ) ( x ) = ....

Jika dan  , maka  ....

Iklan

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Iklan

Pembahasan

Pembahasan
lock

Jika dan , kita menggunakan sifat invers fungsi komposisi : kita cari dulu fungsi komposisinya kemudian kita cari inversnya : jadi, jawabannya E

Jika dan  ,

kita menggunakan sifat invers fungsi komposisi :

size 14px left parenthesis size 14px g to the power of size 14px minus size 14px 1 end exponent size 14px ring operator size 14px f to the power of size 14px minus size 14px 1 end exponent size 14px right parenthesis size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals begin mathsize 14px style left parenthesis f ring operator g right parenthesis end style to the power of size 14px minus size 14px 1 end exponent size 14px left parenthesis size 14px x size 14px right parenthesis

kita cari dulu fungsi komposisinya

begin mathsize 14px style open parentheses f ring operator g close parentheses left parenthesis x right parenthesis equals f left parenthesis g left parenthesis x right parenthesis right parenthesis end style

               begin mathsize 14px style equals f open parentheses fraction numerator 2 x over denominator x plus 1 end fraction close parentheses equals open parentheses fraction numerator 2 x over denominator x plus 1 end fraction close parentheses plus 1 equals fraction numerator 2 x over denominator x plus 1 end fraction plus fraction numerator x plus 1 over denominator x plus 1 end fraction equals fraction numerator 3 x plus 1 over denominator x plus 1 end fraction end style

kemudian kita cari inversnya :

begin mathsize 14px style y equals fraction numerator 3 x plus 1 over denominator x plus 1 end fraction y x plus y equals 3 x plus 1 y x minus 3 x equals 1 minus y x left parenthesis y minus 3 right parenthesis equals 1 minus y x equals fraction numerator 1 minus y over denominator y minus 3 end fraction open parentheses f ring operator g close parentheses to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 1 minus x over denominator x minus 3 end fraction end style

size 14px left parenthesis size 14px f size 14px ring operator size 14px g size 14px right parenthesis to the power of size 14px minus size 14px 1 end exponent size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals fraction numerator size 14px 1 size 14px minus size 14px x over denominator size 14px x size 14px minus size 14px 3 end fraction size 14px equals fraction numerator size 14px x size 14px minus size 14px 1 over denominator size 14px 3 size 14px minus size 14px x end fraction

jadi, jawabannya E

Fungsi Komposisi

Fungsi Invers

Invers Fungsi Komposisi

Latihan Soal Fungsi Komposisi dan Invers

Latihan Bab

Perdalam pemahamanmu bersama Master Teacher
di sesi Live Teaching, GRATIS!

84

Iklan

Iklan

Pertanyaan serupa

2. Fungsi f : R → R dan g : R → R didefinisikan oleh f ( x ) = 2 x + 11 dan g ( x ) = 1 − x . Tentukan: c. ( g ∘ f − 1 ) ( x )

59

0.0

Jawaban terverifikasi

Iklan

Iklan

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Fitur Roboguru

Topik Roboguru

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2023 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia