Iklan

Iklan

Pertanyaan

Diketahui f − 1 ( x ) = 5 x − 1 2 x ​ dan g − 1 ( x ) = 7 x + 4 3 ​ . Jika diketahui ( g ∘ f ) − 1 ( x ) = 2 , tentukan nilai x !

Diketahui  dan . Jika diketahui , tentukan nilai !

Iklan

D. Nuryani

Master Teacher

Mahasiswa/Alumni Universitas Padjadjaran

Jawaban terverifikasi

Jawaban

nilai xadalah .

nilai x adalah 8 over 7.

Iklan

Pembahasan

Ingatlah sifat invers berikut: . Berdasarkan sifat di atas, dan diketahui , maka nilai x : Dengan demikian, nilai xadalah .

Ingatlah sifat invers berikut:

open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses equals open parentheses g to the power of negative 1 end exponent ring operator f to the power of negative 1 end exponent close parentheses open parentheses x close parentheses.

Berdasarkan sifat di atas, dan diketahui open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x close parentheses equals 2, maka nilai x :

 table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals 2 row cell open parentheses f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent close parentheses open parentheses x close parentheses end cell equals 2 row cell f to the power of negative 1 end exponent open parentheses g to the power of negative 1 end exponent open parentheses x close parentheses close parentheses end cell equals 2 row cell f to the power of negative 1 end exponent open parentheses fraction numerator 3 over denominator 7 x plus 4 end fraction close parentheses end cell equals 2 row cell fraction numerator 2 open parentheses begin display style fraction numerator 3 over denominator 7 x plus 4 end fraction end style close parentheses over denominator 5 open parentheses begin display style fraction numerator 3 over denominator 7 x plus 4 end fraction end style close parentheses minus 1 end fraction end cell equals 2 row cell fraction numerator begin display style fraction numerator 6 over denominator 7 x plus 4 end fraction end style over denominator begin display style fraction numerator 15 over denominator 7 x plus 4 end fraction end style minus begin display style fraction numerator 7 x plus 4 over denominator 7 x plus 4 end fraction end style end fraction end cell equals 2 row cell fraction numerator 6 over denominator 15 minus 7 x minus 4 end fraction end cell equals 2 row cell fraction numerator 6 over denominator 11 minus 7 x end fraction end cell equals 2 row cell 22 minus 14 x end cell equals 6 row cell 14 x end cell equals cell 22 minus 6 end cell row cell 14 x end cell equals 16 row x equals cell 16 over 14 end cell row x equals cell 8 over 7. end cell end table

Dengan demikian, nilai x adalah 8 over 7.

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

18

Iklan

Iklan

Pertanyaan serupa

Jika f ( x ) = 5 x − 2 dan g ( x ) = 4 x − 3 , maka ( f − 1 ∘ g − 1 ) ( x ) = ....

2

4.8

Jawaban terverifikasi

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

Hubungi Kami

Ruangguru WhatsApp

+62 815-7441-0000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2024 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia