Roboguru

Pertanyaan

Diketahui begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 4 plus 2 x over denominator x minus b end fraction comma space x not equal to b end style. Jika begin mathsize 14px style f to the power of negative 1 end exponent open parentheses negative 2 close parentheses equals 2 f to the power of negative 1 end exponent open parentheses negative 1 close parentheses end style maka nilai b adalah ....

  1. -10

  2. -2

  3. 2

  4. 5

  5. 10

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

jawabannya adalah E.

Pembahasan

Dapat diperiksa bahwa fungsi begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 4 plus 2 x over denominator x minus b end fraction comma space x not equal to b end style bersifat bijektif sehingga berlaku f(x) = y. Kemudian, perhatikan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell fraction numerator 4 plus 2 x over denominator x minus b end fraction end cell row y equals cell fraction numerator 4 plus 2 x over denominator x minus b end fraction end cell row cell y open parentheses x minus b close parentheses end cell equals cell 4 plus 2 x end cell row cell x y minus b y end cell equals cell 4 plus 2 x end cell row cell x y minus 2 x end cell equals cell 4 plus b y end cell row cell x open parentheses y minus 2 close parentheses end cell equals cell 4 plus b y end cell row x equals cell fraction numerator 4 plus b y over denominator y minus 2 end fraction end cell end table end style

Kemudian, dengan menggunakan konsep invers kita punya undefined sehingga

begin mathsize 14px style f to the power of negative 1 end exponent open parentheses y close parentheses equals x f to the power of negative 1 end exponent open parentheses y close parentheses equals fraction numerator 4 plus b y over denominator y minus 2 end fraction f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 4 plus b x over denominator x minus 2 end fraction end style

Maka,

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 open parentheses negative 2 close parentheses end cell equals cell 2 f to the power of negative 1 end exponent open parentheses negative 1 close parentheses end cell row cell fraction numerator 4 plus b open parentheses negative 2 close parentheses over denominator negative 2 minus 2 end fraction end cell equals cell 2 open parentheses fraction numerator 4 plus b open parentheses negative 1 close parentheses over denominator negative 1 minus 2 end fraction close parentheses end cell row cell fraction numerator 4 minus 2 b over denominator negative 4 end fraction end cell equals cell 2 open parentheses fraction numerator 4 minus b over denominator negative 3 end fraction close parentheses end cell row cell fraction numerator 4 minus 2 b over denominator negative 4 end fraction end cell equals cell fraction numerator 8 minus 2 b over denominator negative 3 end fraction end cell row cell negative 3 open parentheses 4 minus 2 b close parentheses end cell equals cell negative 4 open parentheses 8 minus 2 b close parentheses end cell row cell negative 12 plus 6 b end cell equals cell negative 32 plus 8 b end cell row cell 6 b minus 8 b end cell equals cell negative 32 plus 12 end cell row cell negative 2 b end cell equals cell negative 20 end cell row b equals cell fraction numerator negative 20 over denominator negative 2 end fraction end cell row b equals 10 end table end style

Jadi, jawabannya adalah E.

9

0.0 (0 rating)

Pertanyaan serupa

Jika , maka nilai  adalah ....

21

0.0

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