RoboguruRoboguru
SD
SMP
SMA
SBMPTN & UTBK

Diketahui f(x)=x+1; g(x)=2x+1; dan h(x)=3x+1. Nilai (f−1∘g−1∘h−1)(1)=....

Pertanyaan

Diketahui ; ; dan . Nilai ....

F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Pembahasan

Diketahui ; ; dan .

menggunakan sifat invers fungsi komposisi:

begin mathsize 14px style open parentheses f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent ring operator h to the power of negative 1 end exponent close parentheses left parenthesis x right parenthesis equals left parenthesis h ring operator g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end style

kita cari dulu fungsi komposisinya:

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

                      size 14px equals size 14px h size 14px left parenthesis size 14px g size 14px left parenthesis size 14px f size 14px left parenthesis size 14px x size 14px right parenthesis size 14px right parenthesis size 14px right parenthesis size 14px equals size 14px h size 14px left parenthesis size 14px g size 14px left parenthesis size 14px x size 14px plus size 14px 1 size 14px right parenthesis size 14px right parenthesis size 14px equals size 14px h size 14px left parenthesis size 14px 2 size 14px left parenthesis size 14px x size 14px plus size 14px 1 size 14px right parenthesis size 14px plus size 14px 1 size 14px right parenthesis size 14px equals size 14px h size 14px left parenthesis size 14px 2 size 14px x size 14px plus size 14px 2 size 14px plus size 14px 1 size 14px right parenthesis size 14px equals size 14px h size 14px left parenthesis size 14px 2 size 14px x size 14px plus size 14px 3 size 14px right parenthesis size 14px equals size 14px 3 size 14px left parenthesis size 14px 2 size 14px x size 14px plus size 14px 3 size 14px right parenthesis size 14px plus size 14px 1 size 14px equals size 14px 6 size 14px x size 14px plus size 14px 9 size 14px plus size 14px 1 size 14px equals size 14px 6 size 14px x size 14px plus size 14px 10

Selanjutnya kita cari inversnya:

begin mathsize 14px style y equals 6 x plus 10 fraction numerator y minus 10 over denominator 6 end fraction equals x end style

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent ring operator h to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis end cell equals cell fraction numerator x minus 10 over denominator 6 end fraction end cell row blank equals cell fraction numerator 1 minus 10 over denominator 6 end fraction end cell row blank equals cell fraction numerator negative 9 over denominator 6 end fraction end cell row blank equals cell negative 1 comma 5 end cell end table

Sehingga Nilai size 14px left parenthesis size 14px f to the power of size 14px minus size 14px 1 end exponent size 14px ring operator size 14px g to the power of size 14px minus size 14px 1 end exponent size 14px ring operator size 14px h to the power of size 14px minus size 14px 1 end exponent size 14px right parenthesis size 14px left parenthesis size 14px 1 size 14px right parenthesis size 14px equals size 14px minus size 14px 1 size 14px comma size 14px 5

Oleh karena itu, jawaban yang benar adalah C.

101

5.0 (4 rating)

Pertanyaan serupa

Diketahui fungsi f(x)=2x−5, g−1(x)=4x+3​  dan h−1(x)=8x+1 Nilai  (f∘(g∘h))−1(−7) adalah ...

58

0.0

Jawaban terverifikasi

Perhatikan diagram panah berikut. Nilai  adalah ....

16

5.0

Jawaban terverifikasi

Diketahui  . Jika   , maka g−1(x)= ....

26

5.0

Jawaban terverifikasi

Diketahui fungsi f:R→R, g:R→R, dan h:R→R. Jika fungsi f(x)=4−3x2, g(x)=xx+2​​, dan (f∘g∘h)−1(x)=3x​. Tentukan fungsi h(x).

46

5.0

Jawaban terverifikasi

Perhatikan diagram panah berikut. Nilai   adalah ....

7

0.0

Jawaban terverifikasi
Ruangguru

RUANGGURU HQ

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

Coba GRATIS Aplikasi Roboguru

Download di Google Play

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

  • Brain Academy Online
  • English AcademyBaru
  • Skill Academy
  • Ruangkerja

Bantuan & Panduan

Fitur Roboguru

Topik Roboguru

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