Diketahui fungsi f(x)=54x−6​. Invers fungsi dari f(x) adalah …

Pertanyaan

Diketahui fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator 4 x minus 6 over denominator 5 end fraction end style. Invers fungsi dari size 14px f size 14px left parenthesis size 14px x size 14px right parenthesis adalah begin mathsize 14px style horizontal ellipsis end style 

  1. begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 5 x minus 6 over denominator 4 end fraction end style 

  2. begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 5 x plus 6 over denominator 4 end fraction end style 

  3. begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator negative 5 x plus 6 over denominator 4 end fraction end style 

  4. begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 6 x plus 5 over denominator 4 end fraction end style 

  5. begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 6 x minus 5 over denominator 4 end fraction end style 

I. Kumaralalita

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Bentuk umum fungsi invers dari fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals a x plus b end style adalah begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x minus b over denominator a end fraction end style.

Diketahui fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator 4 x minus 6 over denominator 5 end fraction end style atau dapat juga dituliskan dalam bentuk begin mathsize 14px style f left parenthesis x right parenthesis equals 4 over 5 x minus 6 over 5 end style, dengan begin mathsize 14px style a equals 4 over 5 end style dan begin mathsize 14px style b equals negative 6 over 5 end style. Invers fungsi dari size 14px f size 14px left parenthesis size 14px x size 14px right parenthesis dapat dihitung seperti berikut,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator x minus open parentheses negative begin display style 6 over 5 end style close parentheses over denominator begin display style 4 over 5 end style end fraction end cell row blank equals cell 5 over 4 open parentheses x plus 6 over 5 close parentheses end cell row blank equals cell 5 over 4 x plus open parentheses 5 over 4 times 6 over 5 close parentheses end cell row blank equals cell 5 over 4 x plus 6 over 4 end cell row blank equals cell fraction numerator 5 x plus 6 over denominator 4 end fraction end cell end table end style 

Dengan demikian, invers fungsi dari size 14px f size 14px left parenthesis size 14px x size 14px right parenthesis adalah begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 5 x plus 6 over denominator 4 end fraction end style.

Jadi, jawaban yang tepat adalah B.

227

4.6 (12 rating)

Yolina

Mudah dimengerti

Naurah Anindya Zahra

Makasih ❤️

Pertanyaan serupa

F(x)=4x3x+2​ maka F−1(1)=...

38

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 Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

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